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16

No, the hot object itself experiences no relativistic effects. The particles in the object however may well experience time dilation or length contraction. In fact in very hot gases and plasma, ideal gas laws may not always apply due to relativistic effects. These effects are especially noticeable in gases once the kinetic energy or fermi energy (for ...


5

The spacetime interval is a relativistic invariant, and is proportional to the travelers proper time. So in a since you are traveling one second per second, per your own wrist-watch. Every other measurement would be the speed of some other inertial reference system, measured with your clock. Let $s^2 = x^2 + y^2 +z^2- (ct)^2$, where $x$, $y$, $z$ are ...


4

The basis is still $\{|\boldsymbol r\rangle\}$. The abstract Schrödinger equation is $$ i\frac{\mathrm d}{\mathrm dt}|\psi\rangle=H|\psi\rangle $$ where $|\psi\rangle$ is a set of four kets, (with a slight abuse of notation) $$ |\psi\rangle=\begin{pmatrix}|\psi_1\rangle\\|\psi_2\rangle\\|\psi_3\rangle\\|\psi_4\rangle\end{pmatrix} $$ Time is still a ...


2

Photon experience infinite time dilation and hence, time is stationary for it. Does photon experience time  photon travels at c through the three spatial dimensions. All of its velocity is directed through the three spatial dimensions. Thus Brian and Einstein are stating that a photon must be stationary in the fourth dimension. For if the photon had any ...


2

This answer has been hinted at in the others, but it's worth stating their collective knowledge as a succinct one liner that every physicist should know: Electric and Magnetic force only make sense in the light of special relativity if they are unified because if they were thought of as separate entities, then relatively moving observers would reach ...


2

The preferred frame of reference is that of the co-moving reference frame that defines the Hubble flow. In practical terms that can be defined by correcting any velocity for the observer's motion with respect to the cosmic microwave background. Individual peculiar velocities for galaxies (including our own) are measured in hundreds to thousands of km/s. This ...


2

General relativity can be expanded in orders of $G$ and $1/c^2$, so that the lowest order term is Newtonian gravity, the next order term gives the correction to orbits such as Mercury around the sun, and the third order term accounts for the gravi-magnetic field detected by Gravity-B probe. These first three orders, sometimes called N, PN, PPN and PPPN, for ...


2

Just to add some influences of heat on a stationary clock on the surface of a star. Heat is energy, and energy increases the energy-momentum tensor, so effectively increases the mass. With everything else remaining equal, this would increase time dilation. On the other hand, heated bodies increase their volume. The same mass over a greater volume leads ...


1

There is in the comment section some qibble about MV and MeV. If you have one electron in a $6MV$ potential it then picks up $6MeV$ of energy. The question asks what is the mass of the electron, which I am presuming is a relativistic mass. This is due to the total energy $E = K + mc^2$ of the electron. Working in MeV units we have the mass-energy of the ...


1

What is meant is that physical laws are the same between (inertial) reference frames so that if you observe two bodies undergoing an elastic collision then you will experimentally determine that the momentum before the collision is the same as the momentum after the collision. An observer in another frame will also note that in his reference frame, the ...


1

A hot gas will exhibit relativistic effects for its particles. A particular particle will have a time dilation effect between collisions with other particles. If its energy is $E = K + mc^2$, $K$ = kinetic energy, and mass is $m$ the Lorentz gamma factor for that particle is then $\gamma = E/mc^2$. This happens to all of the particles for their energy $E$ ...


1

Let us start from the notion of affine space next focussing on the Euclidean $3$-dimensional physical space and finally coming to Minkowski spacetime. An affine (real) $n$-dimensional space is a triple $(\mathbb A,\vec{\cdot}, V)$, where $\mathbb A$ is a set whose elements are called points, $V$ is a real $n$-dimensional vector space and $\vec{\cdot} : ...


1

All three are "correct", and all three refer to mass-energy equivalence discovered by Einstein. Equations (2) and (3) are algebraically identical, and are generalizations of (1). Equation (1) only takes into account an object's rest mass, whereas equation (2) also takes into account the momentum $p$ of the object, and (3) takes into account velocity $v$. ...


1

It depends on whether the current is carried by a conductor or is in free space (an electron beam). In the case of an electron beam, the current will appear to have reversed in direction if you travel faster than the charge carriers, even without relativistic effects. This web page does the transformation roughly like you have attempted, using a charge ...


1

Reichenbach's original volume, "Axiomatization of the Theory of Relativity", appeared in 1924. It is one of a long string of works that periodically rediscover and/or explore the issue of non-Einstein synchronization in Special Relativity. See for instance this review on "Synchronization Gauges and the Principles of Special Relativity" and refs. therein ...


1

The mistake you made was essentially transforming the force twice. In the frame in which the matter is stationary (I'll call this the primed frame), you correctly found: $F'=q\sigma'/2\epsilon_0$ and in the frame in which the matter is moving (unprimed) you correctly found: $F=q\sigma/2\epsilon_0 \gamma^2$ Since $\sigma'=\sigma/\gamma$ this is: ...



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