# All Questions

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### Path integral formulation of quantum mechanics

I'm a mathematics student with not much background in physics. I'm interested in learning about the path integral formulation of quantum mechanics. Can anyone suggest me some books on this topic with ...
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### What is the difference between weight and mass?

My science teacher is always saying the words "weight of an object" and "mass of an object," but then my physics book (that I read on my own) tells me completely different definitions from the way ...
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### Noticing that Newtonian gravity and electrostatics are equivalent, is there also a relationship between the general relativity and electrodynamics?

In classical mechanics, we had Newton's law of gravity $F \propto \frac{Mm}{r^2}$. Because of this, all laws of classical electrostatics applied to classical gravity if we assumed that all charges ...
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### Does the (relativistic) mass change? Why?

I learned recently that when an object moves with a velocity comparable to the velocity of light the (relativistic) mass changes. How does this alteration take place?
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### What does it mean to say “Gravity is the weakest of the forces”?

I can understand that on small scales (within an atom/molecule), the other forces are much stronger, but on larger scales, it seems that gravity is a far stronger force; e.g. planets are held to the ...
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### Why do all the planets of the solar system orbit in roughly the same 2D plane?

Most images you see of the solar system are 2D and all planets orbit in the same plane. In a 3D view, are really all planets orbiting in similar planes? Is there a reason for this? I'd expect that the ...
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### Cooling a cup of coffee with help of a spoon

During the breakfast with my colleagues, a question popped into my head: What is the fastest method to cool a cup of coffee, if your only available instrument is a spoon? A qualitative answer would ...
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### Quantum Entanglement - What's the big deal?

Bearing in mind I am a layman - with no background in physics - please could someone explain what the "big deal" is with quantum entanglement? I used to think I understood it - that 2 particles, say ...
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### Does someone falling into a black hole see the end of the universe?

This question was prompted by Can matter really fall through an event horizon?. Notoriously, if you calculate the Schwarzschild coordinate time for anything, matter or light, to reach the event ...
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### Comprehensive book on group theory for physicists?

I am looking for a good source on group theory aimed at physicists. I'd prefer one with a good general introduction to group theory, not just focusing on Lie groups or crystal groups but one that ...
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### Are Newton's “laws” of motion laws or definitions of force and mass?

If you consider them as laws, then there must be independent definitions of force and mass but I don't think there's such definitions. If you consider them as definitions, then why are they still ...
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### Why do electron and proton have the same but opposite electric charge?

What is the explanation between equality of proton and electron charges (up to a sign)? This is connected to the gauge invariance and renormalization of charge is connected to the renormalization of ...
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### Virtual photon description of B and E fields

I continue to find it amazing that something as “bulky” and macroscopic as a static magnetic or electric field is actually a manifestation of virtual photons. So putting on your QFT spectacles, look ...
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### Can matter really fall through an event horizon?

This question is closely related to Event horizons without singularities from about a year ago (May 2012), which John Rennie answered nicely and persuasively. My variant of the question is this: ...
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### Schrodinger equation from Klein-Gordon?

One can view QM as a 1+0 dimensional QFT, fields are only depending on time and so are only called operators, and I know a way to derive Schrodinger's equation from Klein-Gordon's one. Assuming a ...
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### Can black holes form in a finite amount of time?

One thing I know about black holes is that an object gets closer to the event horizon, gravitation time dilation make it move more slower from an outside perspective, so that it looks like it take an ...
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### Is time dilation an illusion?

It is said that we can verify time dilation by flying a very accurate clock on a fast jet or spaceship and prove that it registers less time than the clocks on earth. However, the clocks on earth ...
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### Does a photon instantaneously gain $c$ speed when emitted from an electron?

An excited electron looses energy in the form of radiations. The radiation constitutes photons which move at a speed $c$. But, is the process of conversion of the energy of the electron into the ...
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### Does a moving object curve space-time as its velocity increases?

We always hear how gravity bends space-time; why shouldn't velocity? Consider a spaceship traveling through space at a reasonable fraction of the speed of light. If this spaceship, according to ...
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### How can gravity affect light?

I understand that a black hole bends the fabric of space time to a point that no object can escape. I understand that light travels in a straight line along spacetime unless distorted by gravity. If ...
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### The Role of Rigor

The purpose of this question is to ask about the role of mathematical rigor in physics. In order to formulate a question that can be answered, and not just discussed, I divided this large issue into ...
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### Mathematically-oriented Treatment of General Relativity

Can someone suggest a textbook that treats general relativity from a rigorous mathematical perspective? Ideally, such a book would Prove all theorems used. Use modern "mathematical notation" as ...
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### Rigor in quantum field theory

Quantum field theory is a broad subject and has the reputation of using methods which are mathematically desiring. For example working with and subtracting infinities or the use of path integrals, ...
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### Are W & Z bosons virtual or not?

W and Z bosons are observed/discovered. But as force carrying bosons they should be virtual particles, unobservable? And also they require to have mass, but if they are virtual they may be off-shell, ...
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### What conservation law corresponds to Lorentz boosts?

Noether's Theorem is used to related the invariance under certain continuous transformations to conserved currents. A common example is that translations in spacetime correspond to the conservation of ...
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### Why does this object periodically turn itself?

See below gif image taken from here. Or see this Youtube video about 30 sec in. Is this a real effect? Why does it seem to turn periodically? Can it be explained by classical mechanics alone? ...
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### Can one do the maths of physics without using $\sqrt{-1}$?

The use of imaginary and complex values comes up in many physics and engineering derivations. I have a question about that: Is the use of complex numbers simply to make the process of derivation ...
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### Do an action and its Euler-Lagrange equations have the same symmetries?

Assume a certain action $S$ with certain symmetries, from which according to the Lagrangian formalism, the equations of motion (EOM) of the system are the corresponding Euler-Lagrange equations. Can ...
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### Do electrons have shape?

According to the Wikipedia page on the electron: The electron has no known substructure. Hence, it is defined or assumed to be a point particle with a point charge and no spatial extent. Does ...
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### Is it theoretically possible to shield gravitational fields or waves?

Electromagnetic waves can be shielded by a perfect conductor. What about gravitational fields or waves?
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### If I am travelling on a car at around 60 km/h, and I shine a light, does that mean that the light is travelling faster than the speed of light?

The title says it all. If I was on a bus at 60 km/h, and I started walking on the bus at a steady pace of 5 km/h, then I'd technically be moving at 65 km/h, right? So my son posed me an interesting ...
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### Why is the (free) neutron lifetime so long?

A neutron outside the nucleus lives for about 15 minutes and decays mainly through weak decays (beta decay). Many other weakly decaying particles decay with lifetimes between $10^{-10}$ and $10^{-12}$ ...
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### Noether theorem and classical proof of electric charge conservation

How to prove conservation of electric charge using Noether's theorem according to classical (non-quantum) mechanics? I know the proof based on using Klein–Gordon field, but that derivation use ...
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### What would be the effects on theoretical physics if neutrinos go faster than light?

Earlier today, I saw this link on Facebook about neutrinos going faster than the speed of light, and of course, re-posted. Since then, a couple of my friends have gotten into a discussion about what ...
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### Redshifting of Light and the expansion of the universe

So I have learned in class that light can get red-shifted as it travels through space. As I understand it, space itself expands and stretches out the wavelength of the light. This results in the light ...
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### Shape of the universe?

What is the exact shape of the universe? I know of the balloon analogy, and the bread with raisins in it. These clarify some points, like how the universe can have no centre, and how it can expand ...
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### Born rule and unitary evolution

Is the Born rule a fundamental postulate of quantum mechanics, or can it be inferred from unitary evolution?
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### Rotate a long bar in space and get close to (or even beyond) the speed of light $c$

Imagine a bar spinning like a helicopter propeller, At $\omega$ rad/s because the extremes of the bar goes at speed $$V = \omega * r$$ then we can reach near $c$ (speed of light) applying some ...