# Tagged Questions

The special theory of relativity describes the motion and dynamics of objects moving at significant fractions of the speed of light.

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### Why is $d^4p$ “obviously” Lorentz invariant?

Is there a mathematical and a physical reason? I believe it follows from the jacobian of the Lorentz transformation. But, if that is so, I don't see why it would be "obvious" unless you can do such ...
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### why do x Schwarzschild radii equal time dilation effects of speed of light going y times faster than an object^2?

let me walk you through the math. First you start with the gravitational time dilation formula where: $$T_1=T\sqrt{1-\frac{2GM}{rc^2}}$$ and rather than entering $r$ for the radius we replace $r$ ...
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### Are the edges of a galaxy moving inwards?

Space is expanding, but as I understand it, galaxies are not since gravity keeps them together. If you think of space becoming bigger, your galaxies just become further apart. But taking the size of ...
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### Finding the final velocity of an accelerated proton using its kinetic energy? [closed]

So. I'm trying to find the final velocity of a proton that is being accelerated by a particle accelerator, just before it collides with a particle. All I have is its kinetic energy just before ...
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### Speed of Light with trains [duplicate]

Suppose that there is a train (train1) going at 100 km/h. The train is infinitely long. Suppose that there is an other train inside train1 (train2), which has a speed of 100 km/h also. So for a ...
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### Feynman lectures on physics: The Michelson-Morley experiment

I have a problem understanding something. I'm reading FLP and here I don't understand why when the system is travelling, the light doen't make the same angle in the mirror C... if B and C are moving ...
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### Are there any well-known large body objects moving at a significant fraction of the speed of light relative to earth?

Introduction I've been reading a book called PsychoPhysics, part of the "Illuminati God Series" by Mike Hockney (a pseudonym). Without getting into too much detail, they basically believe that the ...
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### Proving the conservation of 4-momentum for a particle collision $A+B\to C+D$

Let me say that particle A hits particle B and two particles come out - C and D; In system S I can write: $$p_A^μ+p_B^μ=p_C^μ+p_D^μ;\tag{1}$$ here $p_N^μ$ is the 4-momentum. Using the Lorentz ...
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### Characteristic of photons for constant speed

What characteristic of photons causes them to travel with constant speed in all frames of reference? Till the topics I have studied, we always assume this but never got any ideas what can be in the ...
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### Relativistic explanation of attraction between two parallel currents

This has been answered a lot of times, and I have been reading about it on many websites, including PSE, but I still don't get it. So please don't mark it as a duplicate unless it really is one. Two ...
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### How can a photon “stop”? What does its world line look like? [duplicate]

Einstein famously made a thought experiment: what would he see if he sat on a beam of light? His answer was -- it's impossible. Owing to him being a body with mass, he can never ever reach light speed ...
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### Why don't electromagnetic waves require a medium?

As I understand it, electromagnetic waves have two components which are the result of each other, i.e., when a moving electric charge creates a changing magnetic field at point X then a changing ...
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### How does a laser beam change angle from frame to frame in special relativity?

I am at Point A, and I have a laser pointer. I point it at a mirror, one mile west of me, at point B. The beam travels to the mirror and comes back to make a nice round dot on my shirt at point C. In ...
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### Travelling faster than the speed of light

Let's say I fire a bus through space at (almost) the speed of light. If I'm inside the bus (sitting on the back seat) and I run up the aisle of the bus will I in fact be traveling faster than the ...
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### Relativistic factor between coordinate acceleration and proper acceleration

I did a recent question about relativistic kinematics here: Generalizing a relativistic kinematics formula for spatial-acceleration dependence. I have a confusion. In the textbooks I've seen, they ...
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### Relativistic Kinematics - 2-Body Particle Decay

Consider the scenario where a particle of mass $M$ decays into two lighter particles of mass $m_1$ and $m_2$. In the center of mass frame (i.e. $\mathbf{p}_1$ and $\mathbf{p}_2$, the momenta of the ...
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### Does the force between two point charges change when inertial reference frame changes?

The two point charges are as below: Then the Coulomb force between them is: $$F_1=\frac{q^2}{4\pi\epsilon_0 r^2}$$ When the inertial reference frame moves left at $v$(or the point charges move ...
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### Is each succeeding dimension time? [closed]

I have been researching but I have found nothing on this topic (at least after basic google searching and some deeper searching on this site), I'm not sure if this is a common sense thing or it is ...
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### Relativistic drift velocity of electrons in a superconductor?

Is there a formula for the effective speed of electron currents inside superconductors? The formula for normal conductors is: $$V = \frac{I}{nAq}$$ I wonder if there are any changes to this ...
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### Emitting flash of light at relativistic speed

Let's say we have two observers, one stationary and the other moving at relativistic speeds. The observers agree to emit a flash of light when their clock reads 10 seconds. I think it should be ...
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### Did the mass of the electrons went infinite in the experiment done by William Bertozzi in the 1960s?

it is impossible to accelerate a particle to a speed greater than c, no matter how much kinetic energy we give it In an experiment published in 1964, electrons were accelerated to a large voltage ...
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### Why is the speed of light constant in all inertial frames? [duplicate]

I know this is a physical principle and cannot be derived at from other physical laws. But how can it be arrived at? What observations or what train of thoughts leads to this conclusion? e.g. the ...
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### Can we actually have null curves in Minkowski space?

I know that this sounds really stupid but, when I think of the Minkowski space I cannot imagine a null curve, only null lines. For me, the only possible way to have one is to change the basis of the ...
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### General theorems on tachyon propagation?

I was reading the quite nice answer of QMechanic on the topic of compact support tachyon fields not propagating faster than light, but this case is a rather simple one, free scalar field in flat ...
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### Can a pair of members of a “rotating system” be characterized by one value of displacement magnitude?

There seems to be a claim (cmp. Goldstein, "Classical Mechanics", eq. (4-126); or also perceptable here) that values of "velocity", and of "speed", of some participant, say $P$, can not only be ...
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### If the distance between two objects is increasing with increasing rate, can we determine which object is under influence of force?

Suppose two bodies, A and B, are together in free space. One of them, let’s say- A, accelerates away, then retards, stops, accelerates back and stops again when it reaches B. Although we can see the ...
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### Reaching the speed of light [duplicate]

This is a very elementary question, and I'm sure there's a simple answer. However, I must ask... So I had this random thought... Imagine you had a bullet that would fire an additional bullet. Just ...
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### Lifting an analogy of a pond to question signals at natural or artificial boundaries in space-time [closed]

I conjured up an idea to lift an analogy into the language of QFT and GR. I thought up the universe as a pond with a liquid. If we imagine a liquid poured into some pond (sort of bang and inflation ...
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### What is problematic about the Moving magnet and conductor problem?

The problem is posed as follows: There is a conductor and a magnet in relative motion. This motion induces emf in the conductor. The value of the induced emf is independent of whether it's the ...
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### Gravity and velocity increase and time effects problem

First I must specify I am a math major and not currently taking any classes on physics and this is a casual interest/hobby of mine. Therefore I apologize in advance if my questions seem naive. An ...
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### Tomorrowland movie and tachyons? [duplicate]

Would be possible if tachyonic existed to send info to the past or see the future? since the tachyons according to special relativity could travel to the past? i have searched in wikipedia and the ...
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### Relativity and “light years”

As I understand relativity, time is relative to your velocity, meaning your watch moves slower relative to those who are stationary (relatively) when moving at great speeds. So if that's true then ...
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### Relativistic approach of a car and a train to a crossing: seeming contradiction

Suppose a car is approaching a railroad crossing at a high relativistic speed, while on the tracks, a square rail car is also approaching the crossing at the same speed. (The road and the railroad ...
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### Why collide a moving particle with a particle at rest, rather than two moving particles?

I was just reading some lecture notes about relativistic and quantum mechanics, and in the later part of this page the author demonstrates that any relativistic particle collision in the "lab" ...
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### Why cannot a perfect clock exist?

I have a question about the reason Feynman gives for why a perfect clock - a clock that remains in sync while in motion with a stationary clock, cannot exist. It is clear why the "light clock" ...
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### Constant Jerk Relativistic Rocket [duplicate]

A quick google search will give many helpful pages and calculators regarding constant acceleration relativistic rockets, but my question is somewhat different. What if jerk is the parameter to be ...
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### Is static gauge quantization of the particle equivalent to covariant quantization?

In the covariant quantization one is able to get directly (from the constraint $p^\mu_\mu+m^2=0$) the Klein-Gordon equation. But if one uses the parametrization $\tau=X^0$ then the Schrodinger ...
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### Prove that the spacetime interval is not invariant under Galilean transformations [closed]

The spacetime interval $(\Delta s)^2 = (\Delta x)^2 + (\Delta y)^2 + (\Delta z)^2 - c^2(\Delta t)^2$ is invariant under the Lorentz transformation and this isn't the case for the Galilean ...
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### Is the double slit experiment valid in all inertial frames?

In a double slit experiment done with particles having mass (say electrons), the results are inferred as being caused by probability waves. The wavelength of these waves is dependent upon the velocity ...
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### Is there a geometric interpretation of the spacetime interval?

In Euclidean space, the invariant $s^2 = x^2+ y^2+ z^2$ is equal to the length square of the position vector $r$. This is easily understood and can be represented geometrically in a graph. On the ...
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### Potential energy in $E_f^2=(mc^2)^2+(pc)^2$?

Let's consider $$E_f^2=(mc^2)^2+(pc)^2$$ where the $mc^2$ is the rest energy due to the rest mass -- in Finnish "lepomassa". $$\sqrt{(mc^2)^2+(pc)^2} - mc^2~=~(\gamma-1)mc^2$$ is the kinetic ...
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### Boosting massless particles

How does one calculate the boost matrix to go from a photon of (standard) four-momentum $k^\mu = (k,0,0,k)$ to $p^\mu = (p,0,0,p)$? (in terms of $|p|/|k|$) Weinberg in his Quantum Field Theory Vol.1 ...
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### What defines the spin of a certain field? (formally)

Update: see the restatement of the question below! I've seen this question over and over through the archive of questions, but so far the closer to an answer was this. But I still don't understand. ...
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### Lagrangian for relativistic massless particle

For relativistic massive particle, the action is $$S ~=~ -m_0 \int ds ~=~ -m_0 \int d\lambda ~(\dot x ^\mu \dot x_\mu)^{\frac{1}{2}} ~=~ \int d\lambda \ L,$$ where $ds$ is the proper time of the ...
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### Does the rest mass energy include the potential energy of the particle?

The potential energy (as far as I have studied - that is, mainly classical physics) depends on the reference level, since its absolute value cannot be calculated. It can therefore be negative as well. ...
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### What is a Lagrangian of a photon? [duplicate]

In sense of classical mechanics+special relativity what is lagrangian of a photon? Lagrangian of a relativistic massive particle is as follows: $$L_{massive}= -mc\sqrt{c^2-v^2}$$ So is it a zero?
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### Does constant acceleration (from starship crew pov) to relativistic speeds look newtonian?

The last 25 years I thought that time dilation, mass increase and length contraction is "scaled" that way that on the first glance the crew of an accelerating starship could think everything is ...
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### Potential energy in Special Relativity

In Special Relativity, the energy of a free particle is $E^2=p^2c^2+m^2c^4$. But what would be the energy when there is potential energy? If it's something like $E=\sqrt{p^2c^2+m^2c^4}+U$, what ...
### Why is the speed of light a limit? and why is it just $3×10^8\,\text{m/s}$? [duplicate]
Why does light travel with speed $3×10^8\,\text{m/s}$? and why not more?