Lorentz transformations Definition and 175 Threads

lets say you apply a Lorentz boost in the x direction with velocity v and a Lorentz boost in the y direction with velocity v'. Why does it makes that the order in which you apply the transformations affects the resultant transformation matrix? These are two independent directions, so shouldn't...

Can someone explain to me what it means to be "covariant" in the context of special relativity and Lorentz transformations? I already checked wikipedia.

The book I use for relativity states that 4 conditions are required to get the four constants in the lorentz transformations. The 4 conditions the book uses are: 1) velocity of S' seen by S is v. 2) velocity of S as seen by S' is v. 3) Time dilation is same in either frame. 4) Speed of...

Question Show that, with V = 4/5c, the Lorentz transformation of the equations, t^prime = y(V) (t-(v/c^2)x) and x^prime = y(V) (x-Vt). (where y(V) = the Lorentz factor). can be written as ct^prime = 5/3ct - 4/3x and x^prime = 5/3x - 4/3ct Relevant equations y(V) = 1/(sqrt1-(V/c)^2) The...

If a rod is traveling with a velocity 'v' and its proper length is L_0 will the lorentz transformations given below hold true for the length contraction L_0 = \frac {L} { \sqrt {1 - \frac {{v_x}^2} {c^2}}} L_0 = \frac {L} { \sqrt {1 - \frac {{v_y}^2} {c^2}}}

I have studied N.David Mermin "Relativistic addition of velocities directly from the constancy of the velocity of light," Am.J.Phys. 51 1130 1983 and others with the same subject quoted by the Author. He describes a derivation of the addition law that dispenses not only with the LT but also...

I have these past few weeks been steadily studying the different aspects of the theory of Special Relativity. I started with the Lorentz transformations and, thinking I understood them, went along and studied other parts of the theory. However, along the line it has become apparent to me that my...

I state my problem in the following way. Consider the Lorentz transformations x=g(x’+Vt’) (1) t=g(t’+Vx’/c2). (2) They relate the space-time coordinates of the same events E(x,t) and E’(x’,t’) i.e. the space coordinates of the points M(x,0) and M’(x’,0) where the...

I've been going through "Relativity", a translation of a book by Albert Einstein about the Special and General theories of Relativity. It is stressed that the book should be understandable to anyone with a high school education. "A clear explanation that anyone can understand," it says on the...

Is the reason why the Lorentz transformations form a group because of the reason on this website http://en.wikipedia.org/wiki/Lorentz_transformation_under_symmetric_configuration So the group consits of 3 matrices, {identity, forward transformations, inverse transformations}?

All derivations of the Lorentz Transformations I've seen assume a linear transformation between coordinates. Why must this be the case? Thanks.

It is not intuitive, for me at least, why when relating the velocity of 3 inertial frames (Say F1, F2 moving at v1 with respect to F1, and F3 moving at v2 with respect to F2), one mulitplies the transforms of F2 and F3 to get the transform for F1 with respect to F3 to get v3. I understand why v3...

Hi, I have a question about spinors If \Lambda is a Lorentz Transformation what is (and how do you show that it is) the spinor representation of the Lorentz group ? I think it has somnething to do with the equivalence transformation S\dagger{\gamma}S=\Lambda\gamma But that is just a...

Show that \partial'_{\alpha} A'^\alpha (x') = \partial _{mu} A^{\mu}(x') lets focus on the partial operator for now \partial'_{\alpha} = \frac{\partial}{\partial x'^{\alpha}} = \frac{\partial}{L_{\nu}^{\alpha} \partial x^{\nu}} Now A represents the Scalar and vector fields of an EM...

Givne the Lorentz transformations (LTs)}, x'^{\mu} = L_{\nu}^{\mu} x^{\nu} , between the coordinates, x^{\mu} = (ct , \vec{r}) of an event as seen by O, and coordinates, x'^{\mu} = (ct', \vec{r'}) of the same event as seen by an inertial observer O', show that if we write the inverse...

can ne 1 explain 2 me the basics of lorentz transformations...mathematically i know how things transform bt i want a more revealing explanation ...relate it 2 boosts and rotations also ... thanx

Time invariance implies conservation of energy. Space invariance implies momentum convervation. What convervation law does the Lorentz invariance imply?

What is the signifigance of the first derivative of the Lorentz transformation gamma function with respect to dv? What type of system does this derivative represent? \gamma'(v) = \frac{d}{dv} \left( \frac{1}{\sqrt{1 - \left( \frac{v}{c} \right)^2}} \right) = \frac{v}{c^2 \left[ 1 - \left(...

sorry, I'm not particularly well versed in this field. can someone explain the lorentz transformations to me?

Could anyone provide a derivation of the Lorentz transformations for me? And if the Lorentz transformations existed before Einstein came up with special relativity, then why wasn't the Lorentz guy able to come up with special relativity? It seems to me that he did all the work in showing that...

In all the textbooks I read on SR, they always list the LT assuming y'=y and z'=z. But how does the time coordinate transform if the speed has a y and a z component? I'm guessing t' = \frac{t-(v_x x + v_y y +v_z z )/c^2}{\sqrt{1-v^2/c^2}}

Hi , I'd like to know if anybody could help me understand the following: I was following the following derivation of the Lorentz transformations (http://vishnu.mth.uct.ac.za/omei/gr/chap1/node4.html) and i managed to understand everything except possibly the most crucial step...how does one get...

Ok I need some help. I have. t=\frac{t_0}{\sqrt{1-\frac{v^2}{c^2}}} and i rearrange to get: v=\sqrt{c^2(1-\frac{t_0^2}{t^2})} Ok I am setting C=1 tnot = 518400 t = 4.7304 *10^17 as you can imagine my answer i know will be .999999999999 with a lot of 9'sV. The problem is...

Something has me puzzled about the theory of relativity. At time 0, a photon is emitted from the origin of a rectangular coordinate system. At time t, the photon is at position x, on the positive x axis. Therefore in amount of time t-0=t, the photon has traveled a distance of x. The speed...

Hey guys What exactly are the Lorentz transformations? In the "Was Einstein a genius" thread, it looks like the transformations were known before Einstein had SR/GR?