Lorentz factor Definition and 58 Threads

I recently had a look at some textbooks to see how they make use of the Lorentz factor. I have seen that many textbooks introduce γ purely as a mathematical shorthand. On the other hand, some books that delve a little deeper into γ use graphs to show how γ and v are related. I have found...

I’ve been following this recent discussion on the speed of light and its implications in special relativity, and it got me thinking about proper time along light-like curves and the use of the Lorentz factor, ##\gamma##. One point that stood out to me is the claim that proper time along a...

https://ibb.co/Wy9Pq8j I’ve gotten something that looks almost correct, but the expression in the root is 1 + v^2/c^2 instead of minus. I understand intuitively why my answer is wrong, but don’t know where mathematically. Could someone please help me see where I went wrong? Thank you!

Hello everyone, I might be highlighting my ignorance in this post (it might be ignorance of the particulars of simultaneity) but that's a good thing because then I might be able to figure out what I don't know. If the Lorentz factor is 2 for a spaceship that is launched from Earth then...

Hello everyone, I've been learning about length contraction and started to ponder how it applies to space travel. If the Lorentz factor is 2 by traveling at .577c does that mean you would be able to get to the object in half the distance because the transformed length in your reference frame...

This is still a confusing concept for me. The Lorentz transformation for proper time is expressed as tau = (1-v sq/c sq)^1/2 x coordinate time. Now we are told that tau is an invariant quantity with respect to all moving reference frames. So how can tau be invariant if its value depends on v...

I made a derivation of a general transform of the lorentz factor but i still looking in books that the lorentz factor is 1/sqrt(1-v^^2/c^^2) and my derivation is perfectly correct, my result is 1/(sqrt(1-v^^2*sin(a)/c^^2)+v*cos(a)), if we put here 90 degrees we get the classical lorentz factor...

Brief intro: I'm awful at maths and really interested in physics. My friend asked me to solve a question but I can't seem to wrap my head around it... The question: If I'm listening to a song that lasts 5 minutes and 30 seconds and my twin brother travels to the moon and back while the song...

The term "Lorentz transformations" only refers to transformations between inertial frames. However, if we differentiate velocity with respect to time, we obtain acceleration. The Lorentz factor says: t(0 reference frame observer at rest) / t(moving) = 1 / Sqrt[1–(v/c)^2] t0 / tm =...

The Lorentz factor shows how fast one frame will judge speeds in another frame to be taking into account the relative motion between the two frames. The speed of light is a factor in the Lorentz factor but I have heard that this is not because the speed of light is fundamental to it. So...

How do I calculate the Lorentz factor with v=0. Or do I not calculate it since it can be said that the observer is in the same frame of reference?

Hello! This is my first post on this forum, so make sure to tell me if I am doing something wrong :) I was trying to derive the Lorentz factor today, and I used the following page as a guide. The top answer by Jimmy360 is what I followed...

As v approaches c, the Lorentz factor approaches infinity. The math and physics is well understood and observed. Is it true that, just mathematically, as v exceeds c the Lorentz factor approaches 0i for imaginary time constriction?

According to David Morin (link: https://books.google.com/books?id=Ni6CD7K2X4MC&pg=PA636), the time-derivative of the Lorentz factor is (##c=1##): ##\dot{\gamma} = \gamma^3 v \dot{v}##, and the four-acceleration: ##\mathbf{A} = (\gamma^4 v \dot{v}, \gamma^4 v \dot{v} \mathbf{v} + \gamma^2...

Homework Statement There are 2 particles(1,2) separated ∆x=L moving with the same velocity u_x in frame of reference S , there's an other reference S' moving at v . I have to calculate ∆x'. GAMMA(LORENTZ'S FACTOR) Homework EquationsThe Attempt at a Solution I have done x1=0 when t=0 So for...

Hi everyone. Given: an asteroid with the mass of 50,000,000 kg, which is moving with the velocity of oh-my-god particle -- 99.99999999999999999999951% of c. Due to relativistic effects, its total kinetic energy will be 1.44 E+36 Joules (Lorentz factor = 3.2 E+11). A hypothetical particle...

As far as I understand it, the Lorentz factor ##\gamma(\mathbf{v})## is constant when one transforms between two inertial reference frames, since the relative velocity ##\mathbf{v}## between them is constant. However, I'm slightly confused when one considers four acceleration. What is the...

Homework Statement [/B] Two particles of rest mass m0 approach each other with equal and opposite velocity v, in a laboratory frame. What is the total energy of one particle as measured in the rest frame of the other? But the question gives a clue which reads "if (v/c)^2 = .5, then E =...

Homework Statement Perform a Taylor Series expansion for γ in powers of β^2, keeping only the third terms (ie. powers up to β^4). We are assuming at β < 1. Homework Equations γ = (1-β^2)^(-1/2) The Attempt at a Solution I have no background in math so I do not know how to do Taylor expansion...

Homework Statement A rocket ship leaves Earth at 0.6c. The clock of the rocket says 1hr has elapsed. (a.) According to the earth clock, when was the signal SENT? (b.) According to the earth clock, how long after the rocket left did the signal arrive BACK on earth? (c.) According to the rocket...

Homework Statement For a modern physics class, has to do with relativity In a lab experiment a muon is observed to travel 800 m before disintegrating. The mean lifetime of a muon is Tau = 2E-6 s A muon's travel distance at the speed of light is x = tc = 0.66 km Earth's atmosphere is x = 100 km...

Just for my own entertainment I integrated the Lorentz factor with respect to velocity, using basic trig sub, I got the equation arcsin(v/c)*(mc^2). What does this mean? Is it just useless and irrelevant in the physics world or does it have some sort of hidden meaning?

If two particles have velocities v1 and v2 in a rest frame, how do we prove that the relative lorentz factor is given by : γ(r)=γ(1)γ(2)(1−v1.v2) and why is this quantity lorentz invariant

Hi All, Recently, in my earlier thread, I asked about the symmetry of Lorentz Factor (where +V == -V). I had several pointers about how to handle this (Thank you all those). However, it seemed unanimous that there was no explanation beyond the equation itself (math or physical). Also, I...

Homework Statement Find the speed parameter β and Lorentz factor γ for an electron that has a kinetic energy of: a) 6.00 keV b) 2.00 MeV c) 4.00 GeV Homework Equations KE=(γ-1)*511 KeV SQRT(1/(1-β^2))=γ The Attempt at a Solution a) 6 KeV=(y-1)*511 y=1.0117 1.0117=SQRT(1/(1-β^2)) β=0.152 b)...

I had asked this about 2 years ago - but for the life of me cannot find it. Please feel free to cancel this if you can find my OP. Anyhow my question was this: A "train" passes by at significant relativistic speed, along the "x" axis. "Platform" observer peers in windows of train as it passes...

I am hoping someone can help me with something. I want to go into the field of temporal physics and I was wondering if someone could help me understand why Einstein's E=mc2 isn't combined with Lorentz's factor ϒ=1/√1-(v2/c2) to further prove the light-speed barrier?

The question I have for my physics homework is "What does the velocity of an object need to be if it's Lorentz factor is 2?" I know the equation for the Lorentz factor is γ = 1/sq(1-(v^2/c^2)) I just don't know how to get the velocity out of it. I'm a bit of a math and physics noob so that...

Homework Statement Two particles have velocities u, v in some reference frame. The Lorentz factor for their relative velocity w is given by \gamma(w)=\gamma(u) \gamma(v) (1-\textbf{u.v}) Prove this by using the following method: In the given frame, the worldline of the first particle is X...

Lorentz factor for moving inertial reference frames is λ = \frac{1}{\sqrt{1 - \frac{v2}{c2}}}, where v is the relative velocity between the frames. But in my textbook (I'm only just learning relativity), it says the Lorentz factor for a particle is λp = \frac{1}{\sqrt{1 -...

Hello, I've seen several derivations of it and I understand them, specially the one in two dimensions with the right angled triangle, but when I try it in 1 dimension, I always find that the condition that the speed of light is the same in all the inertial frames, isn't enough to specify what...

The Lorentz factor is used ubiquitously in relativity for transformation between frames and in describing various relationships. Wikipedia describes this as: ---------- The Lorentz factor is defined as: γ = 1/√(1-v2/c2) = 1/√(1-β2) = dt/dτ where: v is the relative velocity between...

So I know about the lorentz factor and how it describes time dialition, mass increasing etc.. but I was wondering how it was derived in the first place?

Homework Statement ESTIMATE the Lorentz factor of a spaceship which travels to a nearby star 10pc from the solar system in 50 years spaceship time. Homework Equations Lorentz factor: γ = 1/√(1 - v^2/c^2 ) Time dilation: Δt' = γΔt The Attempt at a Solution Using the distance...

Homework Statement A particle moves such that its relativistic factor γ equals one million. Find β (=v/c). Give answer in the form β = 0.999..., with correct number of nines before first non-nine digit. Do not use a calculator Homework Equations (1-β^2)^(-1/2) = 10^6 The Attempt at...

Is it fair to call the lorentz factor the derivative of measured time relative to proper time? I've seen the lorentz factor equated twice now to \frac{dt}{d\tau} and I wanted to know whether that was a legitimate way to look at it. Thank you

Hello So i saw this video on youtube explaining some basics of general relativity and they used example with 2 rockets moving paralelly with laser pointed from rocket A to mirror on rocket B. Heres my picture of it :D Where we are stationary observer watching those two rockets A and B...

It's not a homework question, but I noticed on this webpage; http://www.relativitycalculator.com/addition_relativistic_velocities.shtml near the very bottom there is a section entitled, "What, therefore, would r & θ appear to be to an observor in relatively moving S'?" Example 1 the...

Homework Statement A star is located 4.2 light years from Earth. At what constant velocity must a spacecraft travel from Earth if it is to reach the star in 3.0 years time? Homework Equations I've been working on this for a couple of days, but I'm not entirely sure which equation to use...

Is Lorentz factor reality true according to the laws of physics?? Hi According to the laws of physics, the speed of light is independent of the speed of its source. In the example whereby there are two observers; one in the train moving at high velocity u relative to the other observer on...

please let me know what is a significance of lorentz factor,and what will happen if lorentz factor is not multiplied in the time equation of lorentz transformation.

I am quite confusing about Lorentz factor and Bondi factor. In special relativity, the change in time of a relatively moving frame and a observer frame can be written as ∆t=∆t'/√1-v2/c2 But if we consider the world line of these 2 frames, the change in time of a relatively moving frame...

If I am at rest and I observe a train moving past me at .9c and then the train fires a projectile at .5c relative to it how fast do I observe the projectile moving? With the speeds given, the lorentz factor is 2.294. I made the incorrect assumtion that I could just take the .5c and divide it...

Hello, Is there a way to find the lorentz factor of a point particle in a curved spacetime in terms of metric elements(diagonal) More specifically I was trying to write energy of a point particle in a curved space. thanks

Can anyone explain how Lorentz factor is defined (the one from theory of diffraction, not special relativity)? I read that intensity of diffracted beam is proportional to Lorentz factor, but I could not find its definition. On what parameters does the Lorentz factor depend? How does the...

System K: x=a t=2a/c x'=2a t'=3a/c I need to figure out in what frame K' will these events appear to occur at the same time? I know the answer is c/2 in the -x direction but finding I'm having a hard time finding the velocity. I really confused on how to get the velocity out from...

I don't understand why the lorentz factor is 1/[1-(v2/c2)]1/2 http://www.softcom.net/users/greebo/dila.jpg clearly you reach something different here.. i really don't get this, I'm sure it's something very simple

One way to derive Lorentz factor is imagining the experiment of the light clock. This experiment is about two observers. One observer is moving at a constant speed on the x-axis and the other observer standing at rest. The observer moving along the x-axis carries a light clock which shoots a...

Homework Statement I have to find a relation for kinetic energy as a function of the lorentz factor, KE(gamma). It can only depend on the lorentz factor or on a constant. Homework Equations E_{tot} = \gamma m_{0} c^{2} E_{tot} = KE + m_{0}c^{2} = \sqrt{p^{2}c^{2} + m_{0}c^{4}} \gamma =...

I've had my second class of Modern Physics and I have some "obvious" doubts that many of you certainly had, although I didn't find anything answering the first doubt on a quick google search. 1)Say I am in an inertial reference frame. I can see that any photon going around me do it at a...