1
vote
2answers
119 views

How a accelerated object sees another accelerated body in Special relativity?

Assume two objects are moving with a constant acceleration $a_1$ and $a_2$, which are the measured accelerations by respective object (or constant force being applied to each of the objects) . My ...
1
vote
0answers
41 views

Are there 'special' cases for when special relativity can be applied for accelerating bodies?

I have the following theoretical situation: A space station modeled as a ring in free space is rotating about its centre point at a high speed. I am trying to work out where time flows slower. From ...
0
votes
1answer
68 views

Acceleration reaches speed of light? [duplicate]

Hi, I am thinking about acceleration. Let's think we have a force of $1$ N and a particle of $1$ kg, then acceleration will be $1$. So the speed gets higher every second and $c$ seconds later, in ...
0
votes
2answers
107 views

Exact definition of momentarily comoving reference frame (MCRF)

Consider a particle $P$ in the framework of special relativity with position $r(t)=(ct,x(t),y(t),z(t))$ respect to an inertial reference frame $\Sigma=(ct,x,y,z;O)$. I need to know if the following ...
0
votes
0answers
56 views

Transformation of a time-dependent acceleration to another frame

How do I transform a time-dependent acceleration between to rest frames? I was given a particular problem and while I found possibilities [1] [2] for acceleration-transformations when the acceleration ...
1
vote
1answer
128 views

Reduction in gravity from photon exchange

Let's say you have two bodies at are held at rest relative to each other exchanging (real, not virtual) photons back and forth. Then we let them go (maybe push them apart slightly), so they will ...
3
votes
4answers
534 views

Why acceleration is not relative in General Relativity?

I was thinking of it, If I say: "I'm moving at a velocity $v_1$ relative to a reference frame $M$ then the acceleration will be the derivative of $v_1$ relative to the reference frame $M$." In other ...
1
vote
2answers
352 views

Derivation of relativistic uniformly accelerated motion

I'm trying to understand solution of the following problem from Landau, Lifshitz, Classical Theory Of Fields: (ending skipped). What I see when I "write out the expression for $w^iw_i$", using ...
3
votes
2answers
138 views

Proper Time with a non-zero Initial Velocity

I have a question regarding how to find the proper time for a body with an initial velocity to slow down to 0. For example, the equation I have been working with looks like: $$\int^\tau_0 ...
5
votes
2answers
288 views

Force in Special Relativity

I have a question regarding how force on a body works in the framework of special relativity. As far as I am aware, the equation for force in special relativity is: $$F=m\alpha$$ Where $\alpha$ is the ...
2
votes
1answer
261 views

Derivation of hyperbolic motion in Special Relativity

My question pertains to the equation of hyperbolic motion in special relativity: $$x^{2} - c^{2}t^{2} = c^{4}/\alpha^{2}.$$ As far as I am aware, this equation is the key to calculating coordinate ...
4
votes
2answers
196 views

Total time taken for an accelerating frame in special relativity [duplicate]

How does one derive the equation for the total time traveled in a constantly accelerating frame? I found some help at this question: Special Relativity and Constant Acceleration But the information ...
2
votes
1answer
506 views

Special Relativity and Constant Acceleration

My question pertains to the concept of a constantly accelerating rocket as it approaches the speed of light. The scenario is as follows: A rocket is constantly accelerating at 1g to reach Andromeda. ...
1
vote
1answer
131 views

Accelerated Light Sources

When someone accelerates towards a light source, how does the light that's radiating off from it look? I suppose in an inertial frame, all the light should be moving off straight from the source, but ...
1
vote
0answers
39 views

Calculate the acceleration of the trailing muon bunch

Two separate suitably short but intense bunches of muons, "A" and "B", are both supposed to be constantly accelerating (in an otherwise sufficiently flat region) with constant proper acceleration ...
1
vote
2answers
129 views

Can acceleration feel like constant gravity for indefinitely long?

So here's the setup: I'm in a spaceship, without windows as always, and the ship is accelerating upwards at a constant rate of $1\,\text{g}$. So inside the spaceship it feels like I'm being pulled ...
2
votes
1answer
343 views

Difference between proper and comoving frames

I'm reading this book "Introduction to Quantum Fields in Classical Backgrounds" by Mukhanov & Winitzki, and there in the chapter 8 "The Unruh Effect" they introduce 3 reference frames. Laboratory ...
2
votes
2answers
180 views

Understanding bending light beam perpendicular to motion

I'm just reading a book about gravity. An example it gives is a spaceship accelerating. A beam of light travelling at right angles to the direction of movement of the spaceship enters it via a small ...
3
votes
3answers
286 views

Why geometrically four acceleration is a curvature vector of a world line? And what is proper acceleration?

Why geometrically four acceleration is a curvature vector of a world line? Geometrically, four-acceleration is a curvature vector of a world line. Therefore, the magnitude of the ...
1
vote
1answer
143 views

Accelerating expansion of universe - entire universe a non-inertial frame of reference?

If the expansion of the universe is accelerating, doesn't that mean that the entire universe is a non-inertial frame of reference? And if so, what implications does this have (if any)?
0
votes
2answers
168 views

Acceleration and relativity

Usually in physics books this equation used $a=\frac {dv}{dt}$ to calculate the relativistic acceleration. It is true that speed $v=\beta c$ don't have relativistic (Lorentz) factor, But time have a ...
2
votes
2answers
388 views

Special Relativity: What differential equation describes an accelerated object from a non-inertial reference frame?

I am looking for a set of differential equations (to be solved numerically for an educational program) that would describe the position and apparent time of an accelerated clock relative to a ...
5
votes
2answers
514 views

relativistic acceleration equation

A Starship is going to accelerate from 0 to some final four-velocity, but it cannot accelerate faster than $g_M$, otherwise it will crush the astronauts. what is the appropiate equation to constraint ...
1
vote
0answers
109 views

maximum distance between accelerating objects started at different times [closed]

Let there be two objects that have zero relative velocity with respect to each other in an inertial frame. If they both undergo identical accelerations, but one starts the acceleration at t = T1 and ...
13
votes
4answers
479 views

Is there an easy way to show that $x^2-t^2=1/g^2$ for a (relativistic) body undergoing acceleration g?

A professor asked me about the (c=1) equation: $$x^2 - t^2 = 1/g^2$$ which I used in a paper. Or with $c$: $$x^2 - (ct)^2 = c^4/g^2.$$ I told him that it was the exact equation of motion for a ...
5
votes
3answers
1k views

Is acceleration relative?

A while back in my Dynamics & Relativity lectures my lecturer mentioned that an object need not be accelerating relative to anything - he said it makes sense for an object to just be accelerating. ...
8
votes
3answers
396 views

Whether $m$ in $E=mc^{2}$ and $F=ma$ are both relativistic mass?

I know that $m$ in $E=mc^{2}$ is the relativistic mass, but can $m$ in $F=ma$ can also be relativistic? If the answer is yes, then can you tell me whether this equation is valid $E=\frac{F}{a}c^{2}$? ...
2
votes
1answer
275 views

Thought experiment about acceleration

Case 1: two people wake up in spaceships accelerating at 1g. They can measure or observe anything inside the room but not outside. They couldn't determine if they were on a spaceship or on earth. ...
8
votes
2answers
2k views

Relativistic centripetal force

The thought randomly occurred to me that a circular particle accelerator would have to exert a lot of force in order to maintain the curvature of the trajectory. Many accelerators move particles at ...
3
votes
4answers
4k views

Ion Drive Propulsion Top Speed

I would like to know if there is some formula / graph which would provide / show the efficiency of a certain type of propeller in space. Specifically, I'm interested in the acceleration attainable at ...
10
votes
5answers
3k views

Acceleration in special relativity

I am currently studying the motion of relativistic charged particles in electromagnetic fields. More exactly, we first derived the equation of motion in the 4-vector formalism. I was a bit confused ...