Recent content by Hacky

I am self-studying and have followed everything in Taylor and Wheel up to the exploded view of the spacetime diagram on page 40. The diagram in lower right hand corner of Fig 23 on page 40 refers to "Events that an observer at A may yet experience if nothing is shrouded from his gaze."...

My understanding is that this experiment would not yield the same result with say two baseballs launched from the center of the train because they would follow classical Galilean addition of velocities (the one launched forward would be moving at the launch velocity plus the velocity of the...

I can understand the logic from some arguments as to why proper time in a photon's "frame of reference" is zero. I cannot understand how this follows from the argument that (SPACE)2 - (TIME) 2 = 0. This to me says that the SPACE-TIME interval for the photon is zero (null interval) and SPACE =...

The spine has static (bone, ligaments, discs...) and dynamic (muscle) stabilizers. Spinal cord injury, if high enough, can cause scoliosis due to paralysis of the muscles that support the spine (think of a radio tower supported by guide wires). However, most cases of scoliosis either have no...

"Bang! The Complete History of the Universe" by Linnot, May, Moore

I think I am getting the gist of it, can anyone point to another reference that uses the same line of reasoning to obtain the Lorentz transform? Thanks. As an aside this really is a nice inexpensive book. It has not been revised since 1982 or so and thus the nomenclature might be a bit off...

The thing about his argument I cannot follow is how he turned the rotation between S and \overline{S} into a translation of -ict tan\alpha. I feel like I get everything in the section except this and thus it seems like the Lorentz transformation magically appears out of nowhere,. He writes all...

Lawden and Lorentz Transform Great idea re the scans. I appreciate your time! Howard

I have been reading DF Lawden's nice book on tensor calculus and relativity. I keep going back to first chapter (p 9-11) as I did not 100% get his derivation of the "special" Lorentz transformation. He writes about a rotational transformation in one plane and then writes about a translational...

I am looking at page 930-931 Of Riley, Hobson, Bence. They go from: e'j,= Sij ei X'i = (S^{-1})ij Xj Define L as inverse of matrix S X'i = Lij Xj, since rotations of coordinate axes are rigid, transformation matrix L is orthogonal, thus the inverse transformation is Xi = Lji X'j and Lik...

I was just reading chapter on Cartesian tensors and came across equation for transformation matrix as function of basic vectors. I just do not get it and cannot find a derivation. I am too old to learn Latex, I uploaded a word document with the equation. Thanks, Howard

Unfortunately they are blocking access to this.

Very basic question but could someone briefly explain why the inner product for complex vector space involves the conjugate of the second vector. Of course if imaginary component is 0 then this reduces to dot product in real vector space. And I see that this definition makes sense to calculate...

Of course I can see that i*(i+1)=(i-1) but is there some way (long division?) to show this in general? To show for example that i = {(2+i)(3+i)/(2-i)(3-i)}. Or to come up with these equivalencies, does one just multiply i by whatever you desire in the later expansion. I am reading about...

I write and review papers, grants in clinical medicine and basic biomedical research. The situation is the same as what you describe in astronomy. A good review (even if it pans your work) can be worth its weight in gold, but all too often it is obvious the reviewer(s) either did not carefully...