What is Lorentz factor: Definition and 56 Discussions

The Lorentz factor or Lorentz term is a quantity expressing how much the measurements of time, length, and other physical properties change for an object while that object is moving. The expression appears in several equations in special relativity, and it arises in derivations of the Lorentz transformations. The name originates from its earlier appearance in Lorentzian electrodynamics – named after the Dutch physicist Hendrik Lorentz.It is generally denoted γ (the Greek lowercase letter gamma). Sometimes (especially in discussion of superluminal motion) the factor is written as Γ (Greek uppercase-gamma) rather than γ.

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  1. C

    B Question about choice of reference frame

    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...
  2. C

    I Space travel question -- Does SR length contraction imply the travel time is half?

    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...
  3. e2m2a

    I Understanding Lorentz Factor & Proper Time Invariance

    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...
  4. TheSurfers12

    I Lorentz Factor Variant: Derivation & Angle Dependence

    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...
  5. E

    B Question about the 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...
  6. B

    I Can the Lorentz factor be modified for non-inertial frames?

    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 =...
  7. G

    B Prove Lorentz Factor w/o Speed of Light

    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...
  8. S

    B Calculating Lorentz Factor with V=0

    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?
  9. DatLemonDoe

    B Deriving Lorentz Factor: An Analysis of Jimmy360's Method

    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...
  10. Chris Miller

    B Can the Lorentz Factor Approach 0i as v Exceeds c for FTL Reference Frames?

    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?
  11. S

    B Derivative of the Lorentz factor

    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...
  12. RealKiller69

    Special relativity and Lorentz factor problem

    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...
  13. S

    Help me find my error in a relativistic kinetic energy calculation

    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...
  14. F

    I Derivative of Lorentz factor and four-acceleration

    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...
  15. K

    Relativistic Energy and Lorentz factor

    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 =...
  16. K

    Performing a Taylor Series Expansion for Lorentz Factor

    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...
  17. C

    A rocket ship leaves earth at a speed 0.6c. When a clock....

    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...
  18. C

    Velocity of a muon if observed travel distance is 800 m?

    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...
  19. A

    Is There a Hidden Meaning in Integrating the Lorentz Factor with Trig Sub?

    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?
  20. CassiopeiaA

    Understanding Lorentz Factor: Proving and Explaining Its Invariance

    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
  21. K

    Exploring Lorentz Factor Symmetry: A 125-Year Mystery

    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...
  22. R

    Speed parameter β and Lorentz factor γ

    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)...
  23. 1977ub

    Time Passes Faster: Moving Frame w/ Many Clocks

    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...
  24. Jorlack

    Understand Einstein & Lorentz: E=mc2 & ϒ Formula

    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?
  25. G

    How do I calculate velocity of an object if I know its Lorentz factor?

    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...
  26. H

    Lorentz Factor for relative velocities

    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...
  27. B

    What's the difference between Lorentz factor for frames and for particles?

    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 -...
  28. G

    Issue with deriving the Lorentz Factor

    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...
  29. A

    What does the Lorentz factor actually mean?

    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...
  30. P

    How was the Lorentz factor derived?

    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?
  31. E

    Estimating the lorentz factor of a spaceship

    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...
  32. D

    Lorentz factor = 10^6, solving for Beta

    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...
  33. Vorde

    Understanding the Lorentz Factor

    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
  34. W

    Noob question about lorentz factor

    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...
  35. Z

    Lorentz factor for particle moving at angle

    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...
  36. Z

    Lorentz Factor / Spacecraft to Star

    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...
  37. L

    Is Lorentz factor reality true according to the laws of physics?

    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...
  38. B

    Lorentz Factor: Significance & Consequences

    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.
  39. P

    Lorentz factor and Bondi factor

    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...
  40. M

    Help Understanding Lorentz Factor

    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...
  41. V

    Finding Lorentz Factor of a Point Particle in Curved Spacetime

    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
  42. L

    What is the definition of Lorentz factor?

    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...
  43. A

    Velocity out of the Lorentz factor

    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...
  44. T

    Help with basic lorentz factor concept

    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
  45. C

    Lorentz factor for slow speeds

    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...
  46. M

    Relation for Kinetic energy and the lorentz factor.

    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 =...
  47. fluidistic

    Lorentz factor equal to infinity + lots of questions

    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...
  48. C

    Compton shift, lorentz factor

    Hello everyone! I've got a problem I've been working on for the past two days and can't seem to figure out. The problem is as follows: Homework Statement Two different experiments use two different wave lengths for the Comptom Shift. The scattered photons wavelengths and scatter angles...
  49. K

    A few questions about the Lorentz factor

    I have only a rudimentary knowledge of the subject and would like more info about: 1) The consequences of faster-than-light speed. I noticed that \gamma would then involve complex numbers, and seeing as complex analysis is definitely more than imaginary, I was wondering what it could...
  50. R

    Is there a simpler way to understand the Lorentz factor?

    Hello, my name is Ivan and I come from Italy, so sorry for my English. I propose a simple argument that leads to the Lorentz factor. It seems to me far more orthodox (of course, I'm talking about the simplifications) of the theorem of Pythagoras to the known motion of the mirror that reflects...
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