Do Dark Energy and the Casimir effect indicate Exotic Matter could exist?

[okabe rintarou]

TL;DR

Dark energy causes repulsive gravity (negative pressure), and the Casimir effect shows localized negative energy density. Do these real-world phenomena indicate that the underlying physics for theoretical "exotic matter" actually exist?

I have a conceptual question about whether certain physical phenomena suggest that exotic matter is possible in our universe.

From my understanding, there are two phenomena that seem to behave inversely to normal matter:

Dark Energy: It is spread evenly throughout the universe (almost like a mist) and causes a repulsive gravitational effect due to its negative pressure.

The Casimir Effect: It demonstrates that it is possible to achieve a localized state of negative energy density (or negative mass density) between two close, uncharged plates.

Since theoretical "exotic matter" is usually described as needing negative energy density or repulsive gravity, do these two real-world phenomena indicate that the underlying conditions for exotic matter actually exist?

 

[Ibix]

I don't think the Casimir effect does, no. My limited understanding is that it can be rewritten as an effect of van der Waals forces, suggesting a rather more prosaic origin, although I'll defer to others on that.

Dark energy, maybe. It depends what it turns out to be. It is possible it isn't anything - that we've miscalculated something and dark energy is actually the gap between our calculations and the calculations we should have done. Or if dark energy is truly a cosmological constant then it might well be a property of spacetime, not a type of stuff in spacetime at all. Or, it may be a kind of exotic matter. So maybe, as I said.

 

[Demystifier]

I don't think the Casimir effect does, no. My limited understanding is that it can be rewritten as an effect of van der Waals forces, suggesting a rather more prosaic origin, although I'll defer to others on that.

Indeed. For a relatively simple explanation why and how Casimir effect originates from van der Waals forces see my https://arxiv.org/abs/1702.03291

There is nothing exotic about negative energies. Negative potential energy arises whenever there is an attractive force, like Newtonian gravity or electrostatic attraction.

 

[renormalize]

Negative potential energy arises whenever there is an attractive force, like Newtonian gravity or electrostatic attraction.

That's not true in general. The attractive force of a harmonic oscillator has positive energy. Attractive central-potentials of the form $k\,r^n$ have positive energy for $n>0$ (e.g., $n=2$ for the harmonic oscillator) and negative energy for $n<0$ (e.g., $n=-1$ for Newtonian gravity).

 

[timmdeeg]

Indeed. For a relatively simple explanation why and how Casimir effect originates from van der Waals forces see my https://arxiv.org/abs/1702.03291

See also Jaffe 2005 https://arxiv.org/pdf/hep-th/0503158

The Casimir force is simply the (relativistic, retarded) van der Waals force between the metal plates.

 

[PeterDonis]

Attractive central-potentials of the form $k\,r^n$ have positive energy for $n>0$ (e.g., $n=2$ for the harmonic oscillator) and negative energy for $n<0$ (e.g., $n=-1$ for Newtonian gravity).

All this depends on where you set the "zero point" of energy--and you've implicitly made different choices for the two cases you describe. For potentials like the harmonic oscillator, you're implicitly setting $E = 0$ at $r = 0$. But for potentials like Newtonian gravity, you're implicitly setting $E = 0$ at $r = \infty$. You can get the sign of either to switch in some range of $r$ by changing where the $E = 0$ point is.

 

[Dale]

I think that you can say that a bound state must have lower energy than an unbound state, regardless of where you set the zero.

 

[renormalize]

I think that you can say that a bound state must have lower energy than an unbound state, regardless of where you set the zero.

But are there any unbound states of the harmonic oscillator, or more generally of any potential of the form $V(r)=k\,r^n$ where $k>0,n>0\,$?

 

[PeterDonis]

But are there any unbound states of the harmonic oscillator, or more generally of any potential of the form $V(r)=k\,r^n$ where $k>0,n>0\,$?

That potential, if you try to think of it as valid for all $r$ out to infinity, is an idealization and never actually happens, just as the $1 / r$ potential of Newtonian gravity, if you try to think of it as valid all the way down to $r = 0$, is an idealization and never actually happens. For any real gravitating body, the form of the potential changes once you're inside the body, so it doesn't go to minus infinity at $r = 0$. Similarly, for any real harmonic oscillator, at some finite $r$ the potential no longer has the form you gave--the spring breaks, or some other new effect comes into play. And in such cases, you can have unbound states of the thing that was bound in the harmonic oscillator potential before.

 

[okabe rintarou]

Thank you for your explanation,but ,can anyone recommend me good books for reference study that topics in further (and bridge my current knowledge to real physics)?

 

[Dale]

Thank you for your explanation,but ,can anyone recommend me good books for reference study that topics in further (and bridge my current knowledge to real physics)?

What is your current level of physics knowledge?

 

[Ibix]

Thank you for your explanation,but ,can anyone recommend me good books for reference study that topics in further (and bridge my current knowledge to real physics)?

Your intro thread says "18 y/o physics enthusiast". Special relativity should be well within your reach - you'll need calculus if you want to consider non-instantaneous acceleration, but just algebra is enough if you only allow things to change speed instantaneously. I like Taylor and Wheeler's Spacetime Physics (free for download via Taylor's website), but others prefer Morin's Special Relativity for the Enthusiastic Beginner (first chapter free for download, the rest about £10, I think). Understanding SR is a vital first step to understanding GR and relativistic quantum field theory.

 

[Sagittarius A-Star]

but others prefer Morin's Special Relativity for the Enthusiastic Beginner (first chapter free for download, the rest about £10, I think).

The relativity (kinematics) chapter of Morins classical mechanics book is also online available:
https://davidmorin.physics.fas.harvard.edu/sites/g/files/omnuum12331/files/2025-10/cmchap11.pdf
via:
https://davidmorin.physics.fas.harvard.edu/books/classical-mechanics

 

[Demystifier]

That potential, if you try to think of it as valid for all $r$ out to infinity, is an idealization and never actually happens, just as the $1 / r$ potential of Newtonian gravity, if you try to think of it as valid all the way down to $r = 0$, is an idealization and never actually happens. For any real gravitating body, the form of the potential changes once you're inside the body, so it doesn't go to minus infinity at $r = 0$. Similarly, for any real harmonic oscillator, at some finite $r$ the potential no longer has the form you gave--the spring breaks, or some other new effect comes into play. And in such cases, you can have unbound states of the thing that was bound in the harmonic oscillator potential before.

Indeed, the harmonic oscillator potential in physics typically arises due to Taylor expansion around a local minimum of the potential
$$V(x)=V(x_0)+(x-x_0)^2 \frac{V''(x_0)}{2}+\ldots$$
so higher terms can be neglected only for small $|x-x_0|$.

 

[okabe rintarou]

What is your current level of physics knowledge?

High school level and slightly undergraduate lectures

 

[Ibix]

High school level and slightly undergraduate lectures

In that case, definitely get a solid grasp on SR - see my post above.

 

[okabe rintarou]

Any recommendations for YouTube channel and , "Is this a bit of an amateur question?"