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232

Things are not empty space. Our classical intuition fails at the quantum level. Matter does not pass through other matter mainly due to the Pauli exclusion principle and due to the electromagnetic repulsion of the electrons. The closer you bring two atoms, i.e. the more the areas of non-zero expectation for their electrons overlap, the stronger will the ...


39

As the universe expands the density of matter goes down. For example if the volume of some specific region of the universe doubles then the density of the matter in that region halves. More precisely, suppose we take the scale factor of the universe, $a(t)$, to be unity right now and we take the current average density to be $\rho_0$, then at a time $t$ the ...


37

What is the meaning of "matter" in physics? It doesn't matter. Sometimes matter means "particles with rest mass". Sometimes matter means "anything that contributes to the stress-energy tensor". Sometimes matter means "anything made of fermions". And so on. There's no need to have one official definition of the word "matter", nothing about the physical ...


36

Research has created antihydrogen, and that is about it for the present as far as antimatter in bulk, which one would need for antiwater.. Scientists in the US produced a clutch of antihelium particles, the antimatter equivalents of the helium nucleus, after smashing gold ions together nearly 1bn times at close to the speed of light. They were gone ...


34

You asked for process. I'm assuming infinite material strength here, as in the piston cannot be stopped (infinite force on an infinite strength material that can resist infinite temperature). Solids will be compressed, resulting in lots of heat as this happens (with infinite pressure, and infinitely strong materials and thus force, the matter will give), ...


31

No, the exact opposite is true. The molecules in a rock don't stay together because they're spending energy. They stay together because of attractive chemical bonds. The molecules have lower energy when they're together than when they're not, so you have to spend energy to break the rock apart, not to keep it together.


29

You've taken this out of context. The context in which Tesla is writing, he's talking about kinetic energy and heat. Just a few sentences previously he states: ...according to an experimental findings and deductions of positive science, any material substance (cooled down to the absolute zero of temperature) should be devoid of an internal movement and ...


28

Anti-matter is a lot less exciting than you probably think. If we could magically change all matter to anti-matter by waving a magic wand then it would make almost no difference. The anti-Dirk could drink an anti-glass of anti-water in exactly the same you drink a glass of water. The anti-water would have the same density, boiling point, ability to dissolve ...


28

The answer is we don't know. I think it is uncontroversial to say that the prediction of singularities by GR is a sign that the theory is failing: we don't expect there actually to be singularities. But we don't have a theory which works (which does not predict singularities in other words) where GR predicts singularities -- such a theory would need to ...


26

I think that sentence shows that Tesla did not quite grasp the results from relativity. This is not unusual, as many physicists required many years to fully accept relativity, but by 1932 (the date of the writing of that text) I would expect it to be already orthodox knowledge. In any case, Tesla is known to have been a self-taught experimental genius and ...


22

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 particle is given by an equation called the geodesic equation: $$ \frac{d^2x^\alpha}{d\tau^2} = -\Gamma^\alpha_{\,\,\mu\nu}\frac{dx^\mu}{d\tau} \frac{dx^\nu}{d\...


18

The pair production process $$\gamma \to e^+ + e^-$$ where a photon creates a positron and an electron is allowed based on conservation of electric charge and number of leptons (number of particles minus number of anti-particles). However it is forbidden by relativistic kinematics: the right-hand side has a rest frame but the the left-hand side does not, so ...


17

Too long for a comment, but on the nomenclature, Fritz Zwicky's observations of other galaxies made it apparent to him that galaxies had to have much more mass than could be seen. The visible stars added together were about 100 times too light to explain their stellar orbital velocity. There had to be a lot of unseen mass to hold the galaxies together. ...


17

At the moment mass is one of the axiomatically defined quantities in the MKS (meter, kilogram, second) system. As with axioms in mathematics, other units can and have been defined and then the (MKS) units become derivative. The theoretical models of physics use mathematics with its axioms, and in addition impose additional axioms and axiomatic statements to ...


15

The answer is no. And to be clear about this: the set of quantum fields in their least energy state, which we call the vacuum, when left to its own devices, in the absence of stuff (including gravitating stuff) does not fluctuate at all. In this context the term 'fluctuation' was introduced by well-meaning physicists in an attempt to draw an analogy ...


15

Yes, mass has a geometrical explanation. The mass of a system is the magnitude or “length” of its energy-momentum four-vector $p=(E,p_x,p_y,p_z)$, using the Minkowski metric $\text{diag}(1,-1,-1,-1)$ of four-dimensional spacetime. This is the standard interpretation of $$m^2=p\cdot p=E^2-p_x^2-p_y^2-p_z^2$$ in units where $c=1$.


14

In answer to the main question, matter does, in fact, "pass" through other matter. Starting from the macro scale (stars , galaxies), down to the micro scale (atoms), it happens all the time. The "free" movement of matter starts to get impeded, as the atoms start making latices (solids, crystals). But even at this scale, as Rutherford demonstrated, matter (...


14

Maybe one day. This idea, at least it's mathematical genesis seems to have begun with Riemann and later Clifford. In 1870 Clifford (a very good mathematician), building upon Riemann gave a lecture stating: 1) That small portions of space are in fact analogous to little hills on a surface which is on the average flat namely that the ordinary laws of ...


13

They taught me that in high school too (i.e., that matter is "mostly empty space.") Only thing is, it's not true. Solid matter is mostly filled with electrons. Yeah, the mass is all concentrated in the relatively tiny nucleii, but the mass is not what photons interact with, and the mass is not what defines the physical and chemical properties of ordinary ...


10

Yes; you can derive mass from the representation theory of the Lie group ${\rm Spin}(3,1)$. It's a long story, but I think I can usefully summarize it. If you need some areas further expanded, please say so in the comments. First, a definition. The Lie group ${\rm SO}(3,1)$ describes the world that we live in according to special relativity. It is the ...


9

Often, when dealing with high-energy (relativistic) particles the rest mass of the particle can be neglected when performing calculations. Use your expression for $p$ from relativistic considerations, plug in the numbers and see the negligible change when you include and neglect to include the mass of the electron. A good tip for when you enter into higher ...


9

He basically shows that a local symmetry of the matter field described by Dirac equation will directly give as a consequence the existence of the gauge boson field, here photon. This is wrong. There are perfectly well-defined theories where you have matter fields but no gauge fields. And vice-versa: we have perfectly well-defined theories of gauge fields ...


9

Please give a meaning of "matter" in Physics that circumvents this circularity. In modern physics, mass is definitely not defined in terms of matter, and there is no circularity. What we classically called mass was really a definition of its effects on and by other objects. We saw this as an intrinsic quality of an object, and definitional in that ...


8

Quick fun analogy: If we think of the expansion of space as a sheet stretching, particles of matter move away from each other. Hooray, as explained several times before. Extending this to 3D, we're basically stretching objects at a very slow rate. 1.62038964 × 10^-17 m/s / meter, to be precise. Thus, a typical person is stretched at about 3x10^-17 meters ...


8

Basically, the reason is that if the matter is to keep a positive mass, the amount of force required to keep the matter distribution stable tends to infinity once the matter is fit within the schwarzschild radius for that given mass. This was proven in a very strong sense, without much in terms of assumptions about the particular form of the metric, by ...


8

I think the colloquial term for that type of plot is "spaghetti diagram" because you have a bunch of lines running across it. It's really the mass fraction as a function of interior mass. From our stellar structure equations, we have that $$ \frac{dm}{dr}=4\pi r^2\rho, $$ which is derived from the mass-continuity equation, so you can relate the radius, $r$ (...


8

I'll convert my comment into an answer, because I think it answers the question: A black hole would form, because eventually you'd surpass the matter's Schwarzschild radius. The Schwarzschild radius of an object of mass $M$ is $$R=\frac{2GM}{c^2}$$ Compress any amount of mass into a sphere with a radius smaller than that and a black hole will form. Now, ...


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