The Question (Submitted July 24, 1997)

Why is it impossible, at this point in time, to convert energy into matter?

The Answer

It happens all the time. Particle accelerators convert energy into subatomic particles, for example by colliding electrons and positrons. Some of the kinetic energy in the collision goes into creating new particles.

It’s not possible, however, to collect these newly created particles and assemble them into atoms, molecules and bigger (less microscopic) structures that we associate with ‘matter’ in our daily life. This is partly because in a technical sense, you cannot just create matter out of energy: there are various ‘conservation laws’ of electric charges, the number of leptons (electron-like particles) etc., which means that you can only create matter / anti-matter pairs out of energy. Anti-matter, however, has the unfortunate tendency to combine with matter and turn itself back into energy.

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— Koji Mukai, with David Palmer, Andy Ptak and Paul Butterworth

— for the Ask an Astrophysicist

— The National Aeronautics and Space Administration (NASA)

2012.10.10 Wednesday ACHK

Second, Einstein’s E = mc^2 is not an equivalence of energy and matter. It is the equivalence of energy and mass (i.e. the number of kilograms). So a unit volume of the empty space carries some mass equivalent to the energy – it’s a mass of a few protons per cubic meter. But the E = mc^2 equation does not imply, in any sense, that the mass equivalent to the energy has to take the form of localized particles. It may be dispersed, much like the cosmological constant – whose generalized form is also called dark energy. The main reason why the vacuum contains mass is that this mass contributes to the curvature of spacetime – the gravitational field of mass – and be sure that dark energy does. That is why it was introduced.

Dark energy, unlike mass, carries a negative pressure, and it’s the real source of the accelerating expansion it induces. Ordinary matter has attractive gravity.

— answered May 3, 2011 at 4:33

— Lubos Motl

2012.10.09 Tuesday ACHK

Many other aspects of quantum geometry or minimal length – such as T-duality, a critical, “maximal” Hagedorn temperature, or some kinds of noncommutativity – do emerge when we approach the smallest distance scales. But the naive discreteness is just one possible way how the usual concepts of a continuous geometry could be realized at short distances. And it is a way that is not chosen in quantum gravity because of many reasons, including its incompatibility with the Lorentz symmetry that we will discuss later in the text.

— Myths about the minimal length

— Lubos Motl

2012.10.04 Thursday ACHK

Many people interested in physics keep on believing all kinds of evidently incorrect mystifications related to the notion of a “minimal length” and its logical relationships with the Lorentz invariance. Let’s look at them.

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— Myths about the minimal length

— Lubos Motl

2012.09.30 Sunday ACHK

Part of our disagreement is a misunderstanding. I am not questioning that the usual notions of geometry break down at the Planck scale (or earlier).

But the reason in string theory is that it does not make sense to talk about shorter distances because the physics at “shorter” distances is not just normal geometry plus something else, but a stringy generalized fuzzy blah blah structure.

Loop quantum gravity, on the other hand, says that geometry is a good variable at all distance scales, and the areas etc. have discrete spectrum, which contradicts Lorentz invariance in any theory with local excitations.

— Lubos Motl

2012.09.26 Wednesday ACHK

Quantization

Poisson brackets deform to Moyal brackets upon quantization, that is, they generalize to a different Lie algebra, the Moyal algebra, or, equivalently in Hilbert space, quantum commutators. The Wigner-Inonu group contraction of these (the classical limit, ) yields the above Lie algebra.

— Wikipedia on Poisson bracket

2012.09.21 Friday ACHK

In physics, certain systems can achieve negative temperature; that is, their thermodynamic temperature can be expressed as a negative quantity on the kelvin scale.

That a system at negative temperature is hotter than any system at positive temperature is paradoxical if absolute temperature is interpreted as an average internal energy of the system. The paradox is resolved by understanding temperature through its more rigorous definition as the tradeoff between energy and entropy, with the reciprocal of the temperature, thermodynamic beta, as the more fundamental quantity. Systems with positive temperature increase in entropy as one adds energy to the system. Systems with negative temperature decrease in entropy as one adds energy to the system.

— Wikipedia on Negative temperature

2012.09.18 Tuesday ACHK

Well, if you pick a particular state in the Hilbert space, it has a well-defined probability if it’s an eigenstate of the density matrix. This is an unusual operation that’s not usually talked about – because the density matrix isn’t an “observable” in the usual sense – like positions or momenta etc. But it’s still an operator on the Hilbert space. I will formally treat the density matrix rho as the “operator for the probability”.

— Density matrix and its classical counterpart

— Lubos Motl

2012.09.13 Thursday ACHK

In my current opinion, each of the three alternative dynamical equations

•     equation for the density matrix
•     Heisenberg equations for the operators
•     Feynman’s path integral

is more pedagogical when it comes to the understanding of the actual relationship between quantum mechanics and classical physics.

— Density matrix and its classical counterpart

— Lubos Motl

2012.09.08 Saturday ACHK

However, most Planck units are many orders of magnitude too large or too small to be of any practical use, so that Planck units as a system are really only relevant to theoretical physics. In fact, 1 Planck unit is often the largest or smallest value of a physical quantity that makes sense according to our current understanding.

For example:

• A speed of 1 Planck length per Planck time is the speed of light in a vacuum, the maximum possible speed in special relativity;
• Our understanding of the Big Bang begins with the Planck Epoch, when the universe was 1 Planck time old and 1 Planck length in diameter, and had a Planck temperature of 1. At that moment, quantum theory as presently understood becomes applicable. Understanding the universe when it was less than 1 Planck time old requires a theory of quantum gravity that would incorporate quantum effects into general relativity. Such a theory does not yet exist;   
• At a Planck temperature of 1, all symmetries broken since the early Big Bang would be restored, and the four fundamental forces of contemporary physical theory would become one force.

— Wikipedia on Planck units

   
   
2012.09.05 Wednesday ACHK