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This is what happens when physicists try to do group theory but don't bother introducing the proper mathematical notions. There is no isomorphism between $\mathrm{SO}(1,3)$ and $\mathrm{SU}(2)\times\mathrm{SU}(2)$, the former is non-compact, the latter is compact. More around this apparently confusing topic can be found in this answer. Furthermore, using ...

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No, in our own frame (comoving frame) we are not moving at all. Even though the CMB radiation is defining a preferred frame, to us it looks like the CMB is moving with respect to us - that's why we see a kinematic dipole in the CMB maps: http://scienceblogs.com/startswithabang/2013/06/28/our-great-cosmic-motion/

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You're both half right. Your teacher is thinking of the invariant mass or rest mass(see footnote [1]), which is thinking in the more modern and much simpler paradigm of naming properties of a particle-like "thing" in a frame of reference at rest relative to that thing and you're thinking of the transformations of the properties to effective values as seen ...

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Your question contains a contradiction because you propose: elementary point particles, in contact with each other but by definition point particles have zero size and cannot be placed in contact with each other. As far as we know elementary particles are indeed pointlike, so you can't have a rod of a finite length made up from elementary particles in ...

2

Plane waves are fully compatible with special relativity, since they are Lorentz-invariant objects: $$\psi_k(x) = e^{i px/\hbar} = e^{i(Et-\vec{p}\cdot\vec{x})/\hbar}$$ You seem to be concerned with the fact that plane waves are spread through all space. But in fact, they're spread through all spacetime! They are perfectly periodic both in space and in time,...

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Yes - these experiments have been conducted, most famously by Aspect et al., but also by others, see Wikipedia. They all observed violations of Bell's inequalities - Our world is therefore not local-realistic in the sense of Einstein. An extension of Bell's inequalities by Legett (Legett inequalities) holds for non-local realistic theories. Their violation ...

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The elementary particles in a piece of normal matter are not in contact with one another; they are in fact very distant from one another compared to their size. But let's imagine some hypothetical matter made of rigid spheres in contact. The length contraction will affect the spheres as well, so they will deform into spheroids (shortened along the direction ...

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Length contraction occurs due to the high relative speed of the reference frames in which the observation is made. When you measure the length of a rod that you hold at rest in your hands the length that you measure is called the proper length. A meter rule of proper length 1.0 m has a length of 0.44 m according to an observer moving parallel to it at a ...

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So you have proper time and proper length. Use rapidity, $\eta$. For proper length $x$ and proper time $\tau$- $\eta=\sinh^{-1}{(\frac{1}{c}{\frac{dx}{d\tau}})}=\tanh^{-1}{(\frac{1}{c}{\frac{dx}{dt}})}$ From this you can calculate the velocity $\equiv dx/dt$

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The other answers saying that true plane waves don't exist and are mathematical idealizations are perfectly true, but you can certainly have waves that are near enough to plane in reality to give rise to the "problem" you allude to. This is where we meet a subtlety to the oft-cited, but somewhat mashed assertion that nothing can travel faster than light. ...

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First of All, I am confused by your question. Light travels at a constant speed in all reference frames. What is this "stationary observer in the Aether Field"? That doesnt make any sense to you or me. Forget about that. The experiment supports the non existence of a medium through which light moves in because of the null result. If you look back to ...

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Plane waves are not real, they are just a mathematical device. In quantum mechanics, particles are represented by wave packets, which do not have infinite amplitude and allow a collection of plane waves to group together by interfering constructively within a certain area and destructively outside that area. From Wikipedia Wave Packets In physics, ...

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What would occur if an electron at rest was accelerated to the speed of light? Any charged particle can be accelerated its speed increasing as more energy is supplied, but the limit of the speed is the speed of light. At a Lorentz factor ( = particle energy/rest mass = [104.5 GeV/0.511 MeV]) of over 200,000, LEP still holds the particle accelerator ...

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Electrons can be accelerated to the speed of light (or practically to the speed of light). If you accelerate electrons to merely 5 MeV the velocity of 0.996 c where c is velocity of light, and yes if they are accelerated to that velocity they will emit gamma like radiation. Here I would like to clarify that the term gamma radiation is mostly used for the ...

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Special relativity predicts that either clock runs more slowly than the other, as judged from the other clock's system: http://www.people.fas.harvard.edu/~djmorin/chap11.pdf David Morin, Introduction to Classical Mechanics With Problems and Solutions, Chapter 11, p. 14: "Twin A stays on the earth, while twin B flies quickly to a distant star and back. [.....

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Well, I'm not going to tell you my opinion, because that would be irrelevant to the actual science. But, what I can do is assess your premises and conclusions. What you should note first, and I'm unsure if you know this or not already, is that the four dimensions of spacetime are the three spatial dimensions and time. We can define a velocity through the ...

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