# Tag Info

46

By popular demand (considering two to be popular — thanks @Rod Vance and @Love Learning), I'll expand a bit on my comment to @Kieran Hunt's answer: Thermal equilibrium As I said in the comment, the notion of sound in space plays a very significant role in cosmology: When the Universe was very young, dark matter, normal ("baryonic") matter, and light ...

35

From the ideal gas law, we know: $$v_\textrm{sound} = \sqrt{\frac{\gamma k_\textrm{B} T}{m}}$$ Assuming that interstellar space is heated uniformly by the CMB, it will have a temperature of $2.73\textrm{K}$. We know that most of this medium comprises protons and neutral hydrogen atoms at a density of about 1 atom/cc. This means that $\gamma = 5/3$, and ...

31

$$\sin(x) = x-\frac{x^3}{3!} + trigonometric\;fluctuations$$ Above you can see why I don't like the language of "quantum fluctuations" -- what people mean by them is just "terms in perturbation series that we can make classical sense of". Similarly the phrase ... particles pop in and out of existence... Is a yet another naive attempt of describing ...

26

Why is space a vacuum ? Because, given enough time, gravity tends to make matter clump together. Events like supernovae that spread it out again are relatively rare. Also space is big. Maybe someone could calculate the density if visible matter were evenly distributed in visible space. I imagine it would be pretty thin. (Later) Space is big. Really ...

23

Just want to bring up that most answers seem to be taking "space" to be a nice uniform medium. However, even within our own galaxy, conditions vary wildly. Here are the most common environments in the Milky Way: Molecular Clouds, $\rho\sim 10^4\,{\rm atom}/{\rm cm}^3$, $T\sim 10\,{\rm K}$ Cold Neutral Medium, $\rho\sim 20\,{\rm atom}/{\rm cm}^3$, $T\sim ... 20 You aren't creating a vacuum, but you are reducing the pressure in your lungs when you inhale. In effect your lungs are working as a diaphragm pump. When you pull your diaphragm down, and/or expand your chest, this increases the volume inside your lungs. Boyle's law tells us: $$P_0V_0 = P_{\rm inhale}V_{\rm inhale} ,$$ where$P_0$and$V_0$are ambient ... 20 The energy is borrowed from the Heisenberg Uncertainty Principle to create virtual particles and has to be paid back in a very short time.$\Delta{t} \geq \frac{\hbar}{2\Delta{E}}$This is why virtual particles live for very short times (i.e pop in and out of existence). We cannot manipulate this energy. 14 Whether you can extract energy from this or not (and I strongly suspect not) the Casimir effect is a consequence of vacuum fluctuations. Essentially when two metallic plates are very close to each other, the wavelengths of virtual particles that can be created between the plates is restricted and hence there are fewer particles between the plates and ... 13 Meson Production A significant contribution to forward, production of pions and other mesons is the knock-on of quark-pairs from the nucleon sea. Reactions like $$e^- + p \to e^- + \pi^+ + \text{undetected hadronic junk} \,.$$ For one of many more technical set of discussions, see the$f_\pi$collaboration's papers:1 http://inspirehep.net/record/535171 ... 12 Freeze it in liquid helium. Any gas inside will condense out. Spin it quickly then stop it. The internal turbulence of the spinning gas will be visible with a sensitive detector. Apply a short sharp impact to one side. If there is gas inside, the sound energy peak from the sound transiting the gas will be temporally distinct from the spectrum of the sound ... 10 Let's consider the simplest case of a quantum harmonic oscillator, with creation and annihilation operators$a^{\dagger}$and$a$respectively. The ground state of our system is,$\lvert 0 \rangle$which has energy, $$E_0 = \frac{1}{2}\hbar \omega$$ Every time a creation operator acts, the state$\lvert n \rangle \to \lvert n+1 \rangle$, modulo some ... 8 I think the key conceptual hurdle is that the vacuum state is not nothing. Quantum field theory describes matter as excitations in quantum fields. These quantum fields are very strange things, and I don't know of any easy way to explain to a non-physicist what a quantum field is. The key thing is that the quantum fields fill all of spacetime. So a vacuum is ... 8 I take your question as Is there any substance with condensed (solid or liquid) equilibrium phase at zero pressure? No, because of statistical physics. Let's consider two things. (1) The potential energy of interaction between molecules. (2) The thermal energy distribution for molecules. The potential energy of interaction can generally be of any ... 7 It means it's "the end of the line". The vacuum state is, as you correctly say, not the zero state. It has energy content, and physical meaning - it's the state with no particles. Annihilating the vacuum leaves...nothing. Trying to take a particle out of it is not possible - it gives you the zero vector, which does not represent a physical state, since it is ... 7 Particles do not constantly appear out of nothing and disappear shortly after that. This is simply a picture that emerged from taking Feynman diagrams literally. Calculating the energy of the ground state of the field, i.e. the vacuum, involves calculating its so-called vacuum expectation value. In perturbation theory, you achieve this by adding up Feynman ... 7 This creates a point of extremely focused energy at the middle point where the bubble collapses. In theory, this point focuses enough energy to trigger nuclear fusion. It is not currently accepted mainstream science to say that collapsing bubbles focus energy enough to cause nuclear fusion. Temperatures over 10,000K can be acheived, but are still well ... 7 Let us look at the instantons of an ordinary pure Yang-Mills theory for gauge group$G$in four Euclidean dimensions: An instanton is a local minimum of the action $$S_{YM}[A] = \int \mathrm{tr}(F \wedge \star F)$$ which is, on$\mathbb{R}^4$, precisely given by the (anti-)self-dual solutions$F = \pm \star F\$. For (anti-)self-dual solutions, ...

6

The image of space being bent is just an analogy, it is not meant that anything is actually being deformed. Gravity distorts the notion of distance on spacetime, i.e. the presence of matter somehow causes the metric to change. A way to visualize this is to think of spacetime being bent, as you say, but really, spacetime is not made of anything, the idea of ...

6

You need to consider that space is filled with a tenuous plasma, which behaves slightly differently to an ideal gas. First, the electrons will carry sound at a different rate to the heavier protons, but also, the electrons and protons are coupled via the electric field. See: Speed (of sound) in plasma The speed of sound in the solar wind is estimated at ...

6

For 1. In principle, the refractive index of a true vacuum is identically 1. For air at atmospheric pressure, the index is 1.000293 for visible light. Therefore, you should be able to determine the deviations between in refractive angles for a jar filled with air and one under vacuum. Since we're talking deviations on the order of one in ten thousandth, it's ...

5

My current understanding is that the physical reality of vacuum fluctuations, particle-antiparticle pairs being created and then annihilating, is disputed. The Casimir effect is often cited as physical evidence but there's a few authors which have come to dispute that the Casimir effect is convincing evidence for the reality of vacuum fluctuations, as they ...

5

The questions you ask are really difficult to answer. Mass is not a property of space (or space-time itself), but of physical objects in classical physics. In General relativity, it is difficult to speak about mass clearly, there is no good general definitions. Now, there are two naive metaphysics about space-time. The substantivalists think that space-time ...

5

Even in a "perfect vacuum", i.e. barring quantum fluctuations, all fields are present. Their field values just are zero, corresponding to no particles or electromagnetic fields present. Still the fields are there! Therefore, just as a matter wave (which is nothing but a particle), light waves, i.e. waves in the electromagnetic field, can propagate through ...

5

Yes, water still has surface tension in a vacuum. Water/vacuum surface tension is 72.8 dyn/cm experimentally according to Zhang et al. J. Chem. Phys. 103, 10252 (1995). Surface tension is caused by the fact that water molecules in the bulk (not at the surface), are surrounded by other water molecules with which they interact through intermolecular ...

5

I assume you are asking why we are not drawing air out of a balloon like container so as to create the lower density that helium or hot air gives us. The answer is that it is hard to maintain a vacuum with a thin enough, so as to be almost weightless, rigid contaning surface. A balloon with gas inside equalizing the atmospheric pressure with the gas ...

5

Virtual particles refer to actual, nonzero features in the quantum fields of real objects, but they are features that are not particles in many ways so you should not expect anything from their being named "particle". Basically, the idea of virtual particles was invented as a device for when you want to hold on to the particle picture while doing quantum ...

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Virtual particles are far more plausible because of experimental results such as the Casimir Effect which is non classical and predicted as a consequence of the "reality" of virtual particles.

4

Space is sometimes described as a vacuum better than mankind could create in any laboratory. But it is not a vacuum, but a tenuous plasma carrying the interplanetary medium (solar wind). It is also structured, forming the Heliospheric current sheet. This means that space has the characteristics of a plasma. It is electrically conductive, carries magnetic ...

4

Why can't fermions have a non-zero vacuum expectation value (VEV)? Lorentz invariance. If anything other than a Lorentz scalar has a non-zero VEV, Lorentz invariance would be spontaneously broken. For example, suppose we have a Lorentz invariant term in a Lagrangian for a vector $$\mathcal{L} \supset m^2 A_\mu A^\mu.$$ Now suppose the vector obtains a ...

4

The answer kinda is "You can, but why would you". It is indeed possible to extract energy from the vacuum. It has been studied, both theoretically and experimentally, using a variety of metal plates and other Casimiresque gizmos. The problem is just that it basically acts like a spring. To put the Casimir effect in action, you must first approach together ...

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