# Tag Info

29

The typical speed of an air molecule is a few hundred meters per second, while escape velocity from Earth is over 10,000 meters per second. So almost all the air molecules just fall back down. They're affected by gravity just like everything else! We do lose some air molecules this way, though. In particular, hydrogen and helium are lighter, so they move ...

15

Ever since Newton and the use of mathematics in physics, physics can be defined as a discipline where nature is modeled by mathematics. One should have clear in mind what nature means and what mathematics is. Nature we know by measurements and observations. Mathematics is a self consistent discipline with axioms, theorems and statements having absolute ...

12

The boiling water is converting liquid water to gas. Unless this gas is continually removed by the pump, it quickly increases the pressure inside the vessel. This increased pressure will stop the boiling. Setting a lid on the jar gives it a one-way valve. Gas can still escape. If you instead put on a full seal so that gas cannot escape, then it will ...

11

It's by definition. A vacuum state is defined to be Poincaré invariant, since it should not depend on the frame (in special relativistic QFT; you get frame-dependent vacua in QFT in curved spacetime). If it had non-zero momentum, it would not be invariant under rotations and boosts, for instance. For the non-interacting vacuum, you can also easily see ...

11

To answer this we need to talk a bit about how particles are described in quantum field theory. For every type of particle there is an associated quantum field. So for the electron there is an electron field, for the photon there is a photon field, and so on. These quantum fields occupy all of spacetime i.e. they exist everywhere in space and everywhere in ...

10

Air fails to escape into space for the same reason you fail to: gravity. As noted in Kevin's answer, occasionally some do get going fast enough to escape. You would too, if enough stuff hit you hard enough. :) Space is a vacuum (for some definition of vacuum), because vacuum is simply the absence of air/gas pressure, and there aren't enough gas molecules in ...

9

I think the problem in understanding this is the idea of "space being sucked into a black hole." The reality is matter is "sucked" into a black hole. Space is warped around the black whole, but space is not "sucked" into anything. Here's the issue. What is space? You can't touch space (or better, the space-time continuum). So, one view is that space is ...

9

In field theory, there are two vacua. The non-perturbative vacuum $|\Omega\rangle$ and the vacuum of the free theory $|0\rangle$. The wikipedia article makes reference to $|\Omega\rangle$ in terms of $|0\rangle$ and its excitations. The true vacuum is annihilated by the (dressed) annihilation operators, and can be thought of perturbatively in terms ...

7

When we refer to the 3 K of temperature in space, we don't mean atomic vibrations. The so called temperature arises, when you look at the sky and measure the radiation, which comes to us from every direction. If you cancel all stars, galaxies and other major light sources you will still "see" very isotropic microwave radiation. And this radiation is ...

6

Yes, you're wrong. Sound waves are small compressions (oscillations) of an elastic medium, travelling through that same elastic medium (as a wave). Air, liquids or solids are typical elastic media through which sound waves can travel. Vacuum however contains no matter and cannot sustain sound waves at all. Watch this video on a bell in a vacuum jar.

6

@JohnDuffield: I can give you both a correct answer in simple terms and the fairy tale, together with references to an explanation how the fairy tale is related to the real thing! The dry facts are that two real particles (e.g., two photons, or an electron and a positron) are created from the energy in the very strong gravitational field near the horizon of ...

6

Both gravity and electrostatic forces depend on distance ($r$) like $1/r^2$. So changing the separation between 2 atoms changes both forces equally. So whichever force is stronger initially (at any distance) will always be stronger. To determine which is stronger consider the ratio of gravitational to electric force. $$F_g/F_e = 4\pi \epsilon_0 G ... 6 Yes, even tiny objects produce gravitational waves as they move. It's just that their gravitational waves will be way too tiny to measure. Just consider that the recent gravitational wave detection was caused by 2 black holes weighing 36 and 29 times the mass of our sun. Even those enormous black holes only caused a tiny change a thousand times smaller than ... 5 Light is made up of photons that are really neither waves nor particles. Sometimes they appear to behave as particles (see photo-electric effect), sometimes as waves (see e.g. diffraction). You have either remembered poorly or your teacher has taught you badly: electromagnetic radiation (photons) doesn't require a medium and does not behave as a particle ... 5 Energy and momentum are conserved at every vertex of a Feynman diagram in quantum field theory. No internal lines in a Feynman diagram associated with a virtual particles violate energy-momentum conservation. It is true, however, that virtual particles are off-shell, that is, they do not satisfy the ordinary equations of motion, such as$$E^2=p^2 + m^2. ...

5

Sometimes I feel Wikipedia is a funny place... In the article you quote they provide a calculation from our patent application (see, e.g., http://akhmeteli.org/wp-content/uploads/2011/08/vacuum_balloons_cip.pdf ) proving that a homogeneous shell made of any existing material cannot be both light enough to float in air and strong enough to withstand ...

4

The cosmological constant of classical General Relativity and the vacuum (or zero-point) energy are closely related. The cosmological constant is simply a constant term $\Lambda$ in the Lagrangian density for the Einstein-Hilbert action and may be interpreted as an energy density permeating all space. In quantum field theory, one finds that the vacuum can, ...

4

Yes, the vacuum energy of a spacetime lattice with finite spacing and periodic boundary conditions within a box of finite size is finite. One would not call this "quantizing", though, rather discretizing because we are not carrying out any "quantization procedure" in the sense of going from a classical to a quantum system. In this approach, the finite size ...

4

The vacuum is "empty" in every precise sense of the word. What we call "particles" in quantum field theory are states created by so-called annihilation and creation operators, which represent "substracting" and "adding" a particle of a certain type to a state. The free vacuum is by definition precisely the state from which you cannnot substract anything, ...

4

I think there are two different questions here. The first question is "what is spacetime?". This is well covered by the answers to the question Is Space-Time a special form of energy? and there's no need to go into this again. Suffice to say that spacetime is a mathematical object not a physical obect so isn't made of anything. The other question is what ...

4

To understand this one shall take in quantum-mechanical approximation method namely perturbation theory into account. In perturbation theory, systems can go through intermediate virtual states which often have energies different from that of the initial and final states. This is because of time energy uncertainty principle. Consider an intermediate state ...

4

The conventional definition of lightning is a current though a plasma (not necessarily through air as lightning happens on other planets) so in a vacuum there cannot be any lightning. However charge does still flow between electrodes in a vacuum, and from personal experience I know that we can get something very like lightning in the right circumstances. In ...

4

The liquid will vaporize. You can just keep sucking. Will not be able to create a vacuum until all the liquid is gone. If you had a barrier between the two and created a vacuum and then removed the barrier you would have vapor of the vapor pressure of the liquid at that temperature.

4

A liquid-vapor interface is not a static interface, there is a so-called liquid-vapor equilibrium where molecules in the liquid phase are continuously escaping from the liquid into the vapor phase and vice versa vapor molecules are continuously captured by the liquid. In equilibrium, the number of molecules leaving the liquid into the vapor and leaving the ...

3

@ACuriousMind 's answer is pretty straightforward. As an alternate proof consider the following: Note that $\hat P^\mu$ is time-independent$^1$, which means that it commutes with $\hat H$. So it commutes with $\exp[-i\hat HT]\ \forall T\in \mathbb C$. We know$^2$ that $|\Omega\rangle \propto \lim_{T\to\infty} \exp[-i\hat HT]|0\rangle$. Using this, its easy ...

3

Sound waves inside the ship hit the wall and are reflected but also somewhat absorbed by the wall, which makes the wall oscillate. If there was air at the other side of the wall, the oscillating wall would cause sound waves to occur but if there a vacuum there then there's no medium to form sound waves with. So no sound can be transmitted through the wall ...

3

When the thermos is closed, the air at the top of the thermos will be warm relative to the ice-cold water below it. As time proceeds, the two materials that are in contact with each other at the surface of the water will exchange heat due to their different temperatures. This will cool the air. When gasses are cooled they move more slowly and they don't ...

3

I think one has to be very careful when talking about "particles popping in and out of existence". This interpretation is only sort of fine in flat-spacetime QFT, where the Minkowski metric is time-invariant, so has a global timeline Killing vector. The definition of a particle depends on the notion of there existing time invariance! Since black hole ...

3

Physical things (solid, liquid, gas, plasma) both absorb and emit energy in the form of electromagnetic radiation of a wide range of frequencies. How fast they radiate and the strongest frequencies of radiation depend on the absolute temperature. How fast they absorb depends on the temperatures of objects around them. Therefore, the net intensity (energy per ...

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