128
votes
Accepted
What does it mean when people say "Physics break down"?
"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 &...
- 6,899
57
votes
If iron can’t undergo fusion, does that mean a black hole is mostly iron?
If we are talking about stellar-sized black holes, then the object that collapses to form a black hole will have a high concentration of iron (and other iron-peak elements like manganese, nickel and ...
- 128k
51
votes
What does it mean when people say "Physics break down"?
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 ...
- 19.8k
49
votes
Accepted
Big Bang and the Pauli Exclusion Principle
The key confusion is the idea that Pauli Exclusion prevents any two particles from occupying the same space. The actual Pauli Exclusion Principle is slightly different: it prevents any two particles ...
- 4,930
48
votes
Accepted
Are black holes very dense matter or empty?
The phrase black hole tends to be used without specifying exactly what it means, and defining exactly what you mean is important to answer your question.
The archetypal black hole is a mathematical ...
- 351k
43
votes
Accepted
What does an undefined formula in physics mean?
Yes, the particle would continue to accelerate and would never reach a terminal velocity. But that is not what this equation tells you. This equation tells you what the terminal velocity is, given the ...
- 1,392
43
votes
If iron can’t undergo fusion, does that mean a black hole is mostly iron?
Iron can undergo fusion. However, iron is the point where fusions starts to cost more energy than it yields, so in a typical star it doesn't fuse.
In a supernova, and the abundance of energy ...
- 560
41
votes
Accepted
Why doesn't physics like infinity (or does it)?
There's no rule against infinity, only a rule against being empirically wrong. Historically, the infinite has hinted we're missing something, but so have plenty of other things too. Let's discuss some ...
- 24.7k
41
votes
Accepted
I'm missing the point of renormalization in QFT
Here's the thing: renormalization and divergences have nothing to do with each other. They are conceptually unrelated notions.
Renormalization
Simply put, renormalization is a consequence of non-...
37
votes
How does Planck's curve solve the ultraviolet catastrophe?
The Planckian approaches zero fast enough: there can be some very high energy photons in a thermal distribution, but the probability of their presence drops fast; crucially, it drops faster than the ...
- 4,907
37
votes
Accepted
If black holes are just empty vacuum of space inside, then what causes the curvature?
GR describes curvature as being caused by stress-energy.
This statement is slightly wrong and is the cause of your confusion here.
Technically, in GR the stress energy tensor is the source of ...
- 94.4k
34
votes
Accepted
How does it make sense for the universe to have started from a big bang?
The singularity at the start of the universe in the Big Bang model is not supposed to be understood as part of the smooth manifold of spacetime, precisely for this reason.
The time function on ...
- 122k
30
votes
Why are we scared of singularities?
"To me it seems like negative or complex numbers. We used to hate these things but now they are more generally accepted. "
Indeed. And in a general context, the infinite answer that some equations ...
- 87.7k
27
votes
Intuitively, why do attempts to delay hitting a black hole singularity cause you to reach it faster?
Actually, it turns out to be incorrect that the optimal strategy is to free fall. There is an optimal strategy for firing your rocket engine which maximizes your proper time from the event horizon to ...
- 94.4k
27
votes
Accepted
Do black holes exist in 1+1 dimensional spacetime?
Black holes are solutions of vacuum EFE on a space-time with singularities.
EFE in the vacuum are:
$$
G_{\mu \nu} = R_{\mu \nu} - \frac{1}{2} R g_{\mu \nu} = 0.
$$
These are sometimes written as
$$
R_{...
- 15.7k
26
votes
Accepted
How can electric field be defined as force per charge, if the charge makes its own, singular electric field?
It's true that a point particle with finite charge is problematic in electromagnetism because of the infinite field and associated energy near such a particle. However, we don't need that concept in ...
- 56.6k
25
votes
What is exactly the density of a black hole and how can it be calculated?
The obvious interpretation of black hole density is the mass of the black hole divided by the volume inside the event horizon. We need to be a bit cautious about taking this too literally because the ...
- 351k
23
votes
Accepted
Where does matter go after reaching singularity in uncharged black holes?
Strictly speaking geodesic incompleteness doesn't mean the worldline of the particle ends at the singularity, but rather that we can't predict what happens to it. The trajectory of a freely falling ...
- 351k
23
votes
Accepted
How do physicists deal with fields at the location of charges?
This problem is nowadays referred to under the names 'self-force' and 'radiation reaction'. In classical electromagnetism it can be solved by noticing that the standard concepts (Maxwell's equations ...
- 56.6k
23
votes
Work done in assembling a point charge is infinite
“Embarrassing” is an opinion, and Griffiths generally has very well-respected opinions. However, as opinions are not facts it is not necessary for everyone to share them.
To me, it is not an ...
- 94.4k
23
votes
What does it mean when people say "Physics break down"?
"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 ...
- 45.6k
23
votes
How does it make sense for the universe to have started from a big bang?
A “singularity” is shorthand for “a place where our current understanding of the laws of physics breaks down”. If we use our current model of the laws of physics (specifically general relativity) to ...
- 47.3k
23
votes
What does it mean for the laws of physics to "break down" at a singularity?
The "laws of physics" are mathematical models that describe the behavior of things in the universe. We use the laws to determine things like how matter moves and how fields interact by ...
- 6,856
22
votes
Why doesn't physics like infinity (or does it)?
Infinity is a shorthand for unbounded. When we say that $\frac 1 x$ goes to infinity as $x$ approaches $0$, what we really mean is that we can make $\frac 1 x$ as large as we like by using a value of $...
- 47.3k
21
votes
Why does the Schrödinger equation work so well for the hydrogen atom despite the relativistic boundary at the nucleus?
In solving the Schroedinger radial equation there is no boundary condition applied at $r=0$. At $r=\infty$ yes, $R(r)$ must tend to zero - so we reject the positive exponential solution; any change ...
- 10k
19
votes
Accepted
Schwarzschild coordinates beyond the event horizon
Coordinates are not sacred objects in GR. Any coordinate system is just as good as any other coordinate system. So to ask whether the Schwarzschild coordinates are valid or not is a meaningless ...
- 351k
19
votes
Does time stop in black holes?
... this should mean that time in the blackhole has stopped completely
Not sure how you reach this conclusion. If we assume that general relativity still applies beyond the event horizon of a black ...
- 47.3k
17
votes
What do the poles of a Green function mean, physically?
Let me expand a little more on what Craig Thone just said :
Consider the energy/frequency-dependent Green function :
$$
\tilde{G}(\omega)=\frac{1}{\omega-(a-\mathrm{i}b)}
$$
with one single pole in $\...
- 2,503
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