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Far field approximation for massive Klein-Gordon equation in 3+1D

You don't need to take $t' \rightarrow +\infty$ and $r' \rightarrow +\infty$ individually. The quantity that should be large is the proper distance i.e. $\sqrt{t' ^{2} - r' ^{2}} \rightarrow +\infty$. ...
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1 vote

Relative velocity of light beam and rocket (special relativity)

It is useful to draw a diagram $t \times x$. Then calculate the equations for the straight lines of the beam and of the rocket trajectory. The interception is the event $t,x$ where the light reach the ...
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0 votes

Moving clocks tick slow and time dilation

The statement that 'moving clocks tick more slowly' is misleading in two important ways. Firstly, if while you sit at your desk reading this you are passed by two spaceships in line, one ahead of the ...
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8 votes
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Is this proof that massless objects cannot be charged?

As was pointed out in the comments above, one has to use relativistic mechanics to talk meaningfully about massless particles; you can't just write $F = ma$ and expect it to work. And, indeed, it ...
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2 votes

Is this proof that massless objects cannot be charged?

I disagree with your conclusion that $qE=0$ if $m=0$. My interpretation is that in such a case the acceleration is infinite, so the product is well defined. It is only natural to think that in ...
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3 votes

Is this proof that massless objects cannot be charged?

I think a massless electron traveling at $c$ under classical Maxwell's Eq. would be problematic, but: The Standard Model says electrons were massless and charged before Spontaneous Symmetry Breaking, ...
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4 votes

Moving clocks tick slow and time dilation

Let’s say Alice measures two events separated in time by ΔtA according to her own watch, and she measures those events in the same place, so she has measured her own proper time. Technically, the ...
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2 votes

Moving clocks tick slow and time dilation

$\Delta t_{B}'$ is the time the moving observer (Bob) measures between the events for which Alice measured $\Delta t_{A}$. Do not conflate this with proper time though. Proper time refers to the ...
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1 vote

Relative velocity of light beam and rocket (special relativity)

But that would imply that it doesn't matter whether the rocket is stationary, or moving at v = 0.8c towards the light beam? What am I missing exactly? You are not missing anything. That is correct. ...
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0 votes

Why do particle accelerators need to smash particles together?

We use particle accelerators to put different kinds of particles close enough together for them to experience interactions, which we can then detect. The easiest way to do this difficult job is to ...
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1 vote

Why do particle accelerators need to smash particles together?

Why doesn’t the kinetic energy produce new particles before the collision? I assume that it is because there is an inertial frame moving with the particles in which they don’t have any more energy ...
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1 vote

Potential energy in Special Relativity

In special relativity, the equation of motion in Galilean coordinates are: $$\frac{\text{d}\boldsymbol{p}}{\text{d}t} - \boldsymbol{F} = \frac{\text{d}}{\text{d}t}\left(\frac{m\boldsymbol{v}}{\sqrt{1-...
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2 votes
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Is four-vector product always Lorentz invariant?

You get scalars only when you fully contract all indices. By contraction here I mean that you sum over all indices using the Einstein summation convention. Within this convention, expressions such as $...
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0 votes

Do objects outside the Hubble sphere violate special relativity?

Dale's answer is wrong, inasmuch as it suggests that this is related to parallel transport in curved spacetime. If you parallel transport two sublight velocities to the same spacetime location and ...
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-2 votes

Isn’t natural units prone to mistakes?

Natural units, philosophically speaking, are the units natural to the problem. If we are measuring the masses of atoms, we are better of measuring in atomic units rather than kilograms. Likewise, if ...
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21 votes
Accepted

Isn’t natural units prone to mistakes?

You are quite correct that the use of natural units removes a useful method for detecting errors. This is an example of a more general concept in information theory. If you use the minimum number of ...
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3 votes

Isn’t natural units prone to mistakes?

Natural units are just a choice of convention/notation which reduces the number of symbols you need to write. It's not an iron-clad safeguard against genuine errors, though it does mean you have fewer ...
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0 votes

Do objects outside the Hubble sphere violate special relativity?

The speed of light is the absolute speed that massless particles like photons can travel at. Such particles are also called luxons. A photon travels in spacetime. However, spacetime in Einstein's GR ...
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2 votes

Do objects outside the Hubble sphere violate special relativity?

Yes, this violates special relativity. Special relativity is only valid in a region of spacetime which is small enough that curvature effects are negligible. The Hubble sphere is not a small region of ...
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1 vote

Why is spacetime in special relativity hyperbolic?

It's an outcome of the absolute nature of the motion of light. But to begin at the beginning ... Since antiquity, the notion of rest and motion were distinct ideas. One was the negation of the other. ...
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3 votes

Doubt about relativity

Matter and [non-gravitational] energy via the stress tensor can cause (or maybe better, “be associated with” [to purposely avoid or postpone the issue of "causation"]) spacetime curvature ...
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0 votes

Are there physics models that accurately handle the assumption of having solutions that achieve finite ending times?

Thanks to the comment by @ConnorBehan about the fast difussion equation, I have been able to find another topics on physics where solutions of finite duration are studied, like sublinear damping, ...
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Doubt about relativity

Matter and energy can both distort spacetime, thereby producing gravity. Einstein's equations of general relativity make this relationship mathematically precise but do not explain why this occurs in ...
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-1 votes

Is Feynman right? Does mass change with speed?

I as an observer move quickly away from an object, is there some sense in which I change its mass? No. You do not change the object in any way by moving away from it. But, if you observe somebody ...
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5 votes

Is Feynman right? Does mass change with speed?

Because speeds are relative to an observer, if I as an observer move quickly away from an object, is there some sense in which I change its mass? This is one reason that modern physicists have ...
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2 votes

Why is spacetime in special relativity hyperbolic?

related: Is spacetime in special relativity hyperbolic? ANS: The spacetime in special relativity is not hyperbolic (is not a [curved] hyperbolic geometry). Similarly, the geometry of Euclidean space ...
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0 votes

Lorentz transformation in GR

I think your question is resolved by the following observation. In a curved space $(t,x,y,z)$ do not in general make a 4-vector, but $(dt,dx,dy,dz)$ do make a 4-vector. In GR you can use a Lorentz ...
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4 votes

Why is spacetime in special relativity hyperbolic?

No, spacetime is not 4 dimensional Euclidean in Galilean relativity; it's 3+1 dimensional, where the time dimension is completely separate from the spatial dimensions and does not mix with them at all....
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0 votes
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Canonical Realization of Poincare Symmetry of Dirac Spinor

I finally realized that my question was really stupid. I don't have to change sign from the Poisson super-bracket. In (pseudo) classical mechanics, given an Lagrangian (second order $L(q,\dot{q})$ in ...
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0 votes

Does time really slow near the speed of light or does it only seem that way to an outside observer?

it is not an illusion but for a referential frame. in my frame time has been slowed down for another it wont and thats where youre wrong. the observer in an inertial frame wouldnt experience any time ...
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1 vote

Does time really slow near the speed of light or does it only seem that way to an outside observer?

No, time really does slow down, and this is established in literally billions of experiments at colliders like the LHC. It's not some kind of optical illusion. Actually, it's probably not helpful to ...
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2 votes

Does time really slow near the speed of light or does it only seem that way to an outside observer?

I'm curious if I came to the correct conclusion You raise a reasonable question - whether the non-intuitive predictions of special and general relativity might be simply due to a time delay in light ...
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0 votes

From a quant-info perspective why are the reals indexing irreps of the Lorentz group less suspect than continuousness in space-time and general QM?

There are three main issues to address here: New theories don't fully retire old ones where they're still useful. For example, if I gave you a throwing-a-ball mechanics problem, you'd neglect not ...
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2 votes

At what constant speed should I travel one light-second to make my time and a stationary person's time 1 second off?

It will depend what speed you are travelling at. However, dealing purely with time dilation effects from special relativity, if it takes you $\tau$ amount of time to travel a certain distance as ...
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0 votes

Is the frequency of photon invariant?

Let's say a photon is approaching from the left at speed c, and an object is approaching from the right at speed -0.87 c. When those two things collide, constant forces F and -F are exerted on them ...
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0 votes

Is the frequency of photon invariant?

Rather than add to or edit my first set of answers (which focused on the Doppler factor as an eigenvalue that was used to scale the 4-momentum of a light-signal and also emphasized that length-...
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0 votes

Is there an official name for "Lorentz Pairs" like energy and momentum?

What you might be looking for is the concept of Lorentz covariance. A Lorentz covariant quantity is a (finite collection of) quantities which are taken to linear combinations of themselves under ...
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4 votes

Is the Dirac Lagrangian a 4-vector?

The Dirac Lagrangian is actually a Lorentz scalar. Remember that $\psi$ is a 4-component spinor and $\bar \psi=\psi^ \dagger \gamma^0$, so everything is contracted nicely such that $L$ is just a ...
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0 votes

Is the frequency of photon invariant?

So once you consider "the source of emission", you are hampering your understanding of the problem: the source of emission is irrelevant. A photon just exists. It moves at $c$ in all frames, ...
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1 vote

Is the frequency of photon invariant?

Lots of answers have provided details, but perhaps more complexity than you were looking for. There are two simple points that answer your question: (1) Energy is always frame dependent. For example, ...
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0 votes

Length Contraction & Accelerating Observers

Let's say we line up million marbles in empty space, distance between two consecutive marbles being 1 light year. We call this line of marbles a "ruler". Now when observer is at rest ...
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0 votes

Relativistic ship and base on Earth talking

Let's say there are two events: A. The pilot starts their message B. The pilot finishes their message In the rocket frame, which we'll call $S^{\prime}$, the time between those events is $\Delta t_{AB}...
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2 votes

Chart transition maps in special relativity

Lorentz transformations are the chart transition maps between charts of different observers That is incorrect. As you mentioned, the same observer can use many different charts. For example, one ...
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0 votes

Chart transition maps in special relativity

In special relativity an inertial observer fixes a time coordinate and the origin in minkowski coordinates. You could say each inertial observer is described by an equivaence class of minkowski ...
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1 vote

Why is proper time equated to $ds$?

This answer considers the generalization of special relativity to general relativity: The infinitesimal arclength $ds$ between 2 infinitesimally close spacetime events/points $P$ and $Q$ on a ...
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0 votes

Chart transition maps in special relativity

That would just be a general coordinate transformation or (in more strict mathematical language) a diffeomorphism. \begin{equation} g'^{\mu \nu} = g^{\alpha \beta} \frac{\partial x'^{\mu}}{\partial x^{...
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7 votes

Why is proper time equated to $ds$?

Generally speaking, the line element can be written as $$ds^2=g_{\mu\nu}(x)dx^{\mu}dx^{\nu},$$ where $g_{\mu\nu}(x)$ are the metric components at the point $(x^0,x^1,x^2,x^3)$. For example, working in ...
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1 vote

Why is proper time equated to $ds$?

In general, the separation between two events contains a spatial component and a time component. If the separation is time like, the time is large and the distance is small. You can travel between the ...
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0 votes

Length Contraction & Accelerating Observers

That calculation of traveled distance consist of two parts: calculate the traveled distance in the launchpad frame transform the result to the traveler frame The second part has nothing to do with ...
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0 votes

What can I substitute for tensors in special relativity?

I suggest you first learn to express calculations vectorially, using vectors and dot-products, together with a visual understanding of what is going on. In addition, for relativity, one should really ...

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