Relativistic Definition and 1000 Threads

How can we know the age of the universe, with time dilation due to the mass and velocity of matter which condensed after the big bang. If time passes at different speeds depending where it is perceived, does this not make the age of the universe somewhat moot.

I once naively think that the speed of light is also a constant in a medium in all inertial frames which is not the case. I tried to derive the result yet there is a discrepancy from the results I read in some articles. For example, from [Link to unpublished paper redacted by the Mentors], the...

Let us consider the co-moving observer ##\mathscr{C}## for whom ##E = \epsilon## and ##\mathbf{\vec{V}} = \mathbf{\vec{0}}##. Doing the perturbation stuff to the first of the relevant equations gives$$\partial_t \delta \epsilon + \boldsymbol{\nabla} \cdot ([\epsilon + p] \delta \mathbf{\vec{V}})...

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In Robert M. Wald's General Relativity he writes on page ##61##: The energy of a particle as measured by an observer - present at the site of the particle - whose 4-velocity is ##v^a## is defined by $$E=-p_a v^a$$ Thus, in special relativity, energy is recognized to be the "time component" of...

I think it is quite simple as an exercise, following the two relevant equations, but at the beginning I find myself stuck in going to identify the lagrangian for a relativistic system of non-interacting particles. For a free relativistic particle I know that lagrangian is...

The answer is tD = [D_0 - 3/4ct - 1/2ct] I just have 2 questions. I realize for 2 vectors approaching it is negative for distance and for velocity positive. What be the rule for time? How do I find vector answers for velocity and distance and time? I am confused why I have "td = ..." ? Can...

I try to use relativistic energy equation: $$E'=\gamma mc^2$$ But, I use $$\gamma=\frac{1}{\sqrt{(1-(\frac{v'}{c})^2}}$$ then I use Lorentz velocity transformation. $$v'=\frac{v-u}{1-\frac{uv}{c^2}}$$ At the end, I end up with messy equation for E' but still have light speed c in the terms. How...

why was the schrodinger equation for the relativistic wave unsuccessful?

Background --- Consider the following thought experiment in the setting of relativistic quantum mechanics (not QFT). I have a particle in superposition of the position basis: H | \psi \rangle = E | \psi \rangle Now I suddenly turn on an interaction potential H_{int} localized at r_o =...

Heres how I tried to set up the problem. I took the laboratory to be S and the frame of the particle whose speed we know to be S', so that the speed of S' relative to S is u = 0.65c. Also, by convention, S' moves to the right of S, so that S moves to the left of S'. Next, we know that the...

I have looked several special relativity books but in each of them the metric is defined as ##\eta_{\nu\mu} = (+1, -1, -1, -1)##. Is there a book where the metric is defined as ##\eta_{\nu\mu} = (-1, +1, +1, +1)## ?

In Quantum field theory by Peskin Schroeder for relativistic normalization δ(p'-q')=δ(p-q) dp'3/dp3 where the boost is in z direction. How did they compute it?

Could this statement be the first step towards quantum gravity? Or is it trivial or not true at all?

Hey! I'm and undergrad in the third year of my applied physics program. I'm taking a course in Special Relativity, and due to Corona the exam has been replaced by a pretty free project where we delve deeply into a topic related to the course. I'm interested in music, so my professor suggested I...

A stationary observer sees a particle moving north at velocity v very close to the speed of light. Then the observer accelerates eastward to velocity v. What is its new total velocity of the particle toward the north-west relative to the observer? I ask because while the particles total...

Is it possible to have some kind of General Relativistic Quantum Theory without passing through the stage of Quantum Field Theory (where Quantum Theory is married to Special Relativity)? Einstein attached primary significance to the concept of general covariance as shown in this letter in 1954...

I'm not sure where to start

Hi! Hope I'm posting this in the right place! I'm practicing for exams and came over this question: A proton with mass ##m_p## is accelerated to a relativistic velocity, with kinetic energy ##K##. It collides completely inelastic with another proton, which has the same kinetic energy, ##K##...

Hello PF. I'm just curious. I found the following description in a textbook I am reading. What I'm interested in here is what would $E$ and $B$ look like if the charge was oscillating at close to the speed of light ( means relativistic velocities) ? Thank you.

In a statistical mechanics book, I learned about the degenerate pressure of a Fermi gas under the non-relativistic regime. By studying the low-temperature limit (T=0), we got degenerate pressure is ##\propto n^{5/3}## (n is the density). And then I was told that in astrophysical objects, the...

Are there any known instances of heat transfer via conduction or convection happening at relativistic speeds? Is this even possible or is there a non-relativistic limit to how fast heat can transfer in these ways, like how sound can only move so fast?

Consider the Hubble horizon as the proper distance over which Hubble expansion equals c, so that you are in the center of a Hubble sphere with a radius of about 13.5 billion light-years. As you approach light speed in any direction, does the Hubble horizon draw closer in that direction due to...

In special relativity (especially relativistic collisions), is the center of mass frame as useful as Newtonian mechanics?

p=Bqr and del p = p del theta

Why can't we interprete /x> in relativistic QFT as position eigenstate?And by the way what is the difference between /x> and /1x>=Phi(field operator)(x)/0>?

I don't know why I'm so puzzled by this problem; it's only one star. So first, I drew a picture of A and B in the ground frame. Then I drew B and the ground in A's frame. I then used the velocity addition formula to obtain the velocities of both B and the ground relative to A. $$\frac{v_{B}^{A}...

I’ve read Beiser’s Modern Physics Chapter 1 and I am able to grasp the general theories but not so much when applying it to problems. I major in Chemistry and would really appreciate any head start/help/suggestions. For number 1 I thought of using L = L0 sqrt 1-v^2/c^2 but can’t seem to find the...

Feynman's Lectures, vol. 1 Ch. 28, Eq. 28.3 is ##r'## is the distance to the apparent position of the charge. Feynman wrote, "Of the terms appearing in (28.3), the first one evidently goes inversely as the square of the distance, and the second is only a correction for delay, so it is easy...

Hi, I was trying to derive relativistic momentum equation using classical momentum equation but it didn't work. Could you please help me? Thank you! Where am I wrong? Or, is not possible, in any way, to derive relativistic momentum using Newtonian momentum equation? Thanks!

Let's take a star 500 light years away from Earth, let's call it Star X. To make round numbers let's say we are in Earth year 2000. We set a manned space mission to Star X, the spaceship will travel at 0.5 light-years per year (0.5 c) so it will reach there in 1000 years. Let's not worry about...

Given that the Minkowski metric implies the Lorentz transformations and special relativity, why do the equations of relativistic quantum mechanics, i.e., the Dirac and Klein-Gordon equations, require a mass term to unite quantum mechanics and special relativity? Shouldn't their formulation in...

$$p=\gamma m v$$ $$F = \frac {md (\gamma v}{dt}$$ $$\int{F dt} = \int{md (\gamma v}$$ $$F t= \gamma mv$$ At this step, I don't know how to make v as explicit function of t, since gamma is a function of v too. Thankss

Hi Pf i am accustomed with the action $$mc \int ds $$ for relativistic particle. i found a paper by Andrew Wipf with another lagrangian. please look at the beginning of chapter seven (7.1) Is it possible to deduce from it the shape of its trajectory? I have a lot of question about this chapter...

Summary:: this is what I've done so far... i don't think it works since i believe the information given is not even enough. the formula I've used are 1. relativistic total energy = rest mass energy + kinetic energy (line 1, 3) 2. conservation of energy (line 4, 7, 8, 9) 3. conservation of...

Hello everyone, I was doing some calculations recently regarding particle velocities for different elements at different temperatures and I have a few questions for the experts in here. Usual gas laws in my school book provides information about the velocity of particles in gases, it provides...

Starting from the center of mass energy S = (E_{1} + E_{2})^2 - (\vec{p_1}+\vec{p_2}) knowing that E^2 = m_{0}c^4 + p^2*c^2 one has S = (E_{1} + E_{2})^2 - (\vec{p_1}+\vec{p_2}) = ( m_{0}c^4 + p_{1}^2*c^2) + m_{0}c^4 + p_{2}^2*c^2)^2 - p_{1}^2 - p_{2}^2 - 2p_{1}p_{2}cos \{theta} and then...

I don't know how to approach this problem.

Wiki said "Arnold Sommerfeld calculated that, for a 1s orbital electron of a hydrogen atom with an orbiting radius of 0.0529 nm, α ≈ 1/137. That is to say, the fine-structure constant shows the electron traveling at nearly 1/137 the speed of light.[9] One can extend this to a larger element with...

Hello guys! I just started to learn Special Relativity though a Stanford youtube channel, and I had some problems already in the first class :oops: The teacher drew a graph with one spatial dimension (x-axis) and one temporal dimension (t-axis). Where X is the horizontal axis, T is the vertical...

**I realize some of my inline math delimiters '\(' and '\)' are not acting on the text for some reason, and it looks clunky. I spend 20-30 minutes trying to understand why this is, but I can't. My limited LaTeX experience is in Overleaf, and these delimiters work fine in that compiler. My...

In deriving the work-energy theorem, Griffiths does the following: ##\frac{d\mathbf{p}}{dt}\cdot\mathbf{u} = \frac{d}{dt}\bigg(\frac{m\mathbf{u}}{\sqrt{1-u^2/c^2}}\bigg)\cdot\mathbf{u}=\frac{m\mathbf{u}}{(1-u^2/c^2)^{3/2}}\cdot\frac{d\mathbf{u}}{dt}## I may have forgotten something essential...

Since initally the rocket at rest I wrote $$\vec{p}^R_i = (m_0, 0,0,0)$$ and at final situation $$\vec{p}^R_f = [m_0-\varepsilon m_0 N](\gamma, v\gamma, 0 ,0)$$ $$\vec{p}^F_f = [\varepsilon m_0 N](\gamma', -u\gamma', 0 ,0)$$ After equating them I get $$1 = \gamma - \varepsilon N\gamma +...

I would like to know what the Special Relativistic versions of Jefimenko's equations are.An example of a noticeable difference between non-relativistic and relativistic cases is considering Jefimenko's equation for the B-field, for a magnetostatic circular current loop. Jefimenko's B-field...

Hello, I consider to be in a relativistic area, where an object is moving very fast, seen from our Earth, at a speed v where v is less than the speed of light c. I have considered the following equations (relativity equations) : T = β * t M = β * m L = l / β β = 1 / (√(1 – v2/c2) )...

My question: How do the values for the velocity, momentum and energy of an electron in a double-slit experiment are altered by the observation? Probably,energy is altered. Given that energy is a function of momentum and velocity, either or both of these must have been changed. However, I am...

How come mercury qualify as a metal, since the 6 s electrons are attracted by the nucleus so strongly because of relativistic effects and unlike other metals there is no cloud of electrons?. Because of this mercury is not a good conductor of electricity unlike other metals

Is it technologically feasible today or in the near future, to accelerate in outer space a ~0.1 gram physics experiment lab, inside a cyclic accelerator and shoot it in a straight line at a constant speed of 5%-80% of the speed of light? That miniature capsule, must include all that is needed...

Hi, Could you please help me with the queries below? Question 1: A GPS satellite is moving faster than the earth, for every day on Earth the clock on the satellite shows one day minus 7 microseconds due to time dilation due to special relativity. However, since the Earth's gravitational pull...