# Questions tagged [special-relativity]

The special theory of relativity describes the motion and dynamics of objects moving at significant fractions of the speed of light.

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### Can you resolve this special relativity paradox?

I've devised a thought experiment called the "Killer Crate Paradox" to further improve my understanding of Lorentz Transformations. This is not a paradox I am able to resolve, so please read ...
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### Thought experiment in Mach's principle - Can a void universe be considered with special relativity?

Mach's principle is based on a thought experiment in which an astronaut floats in the middle of a space devoid of all matter and all landmarks. No star, no source of energy is present, whatever the ...
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### Are time and length independent or can one be derived from the other?

In particular, the time coordinate $t$ can be choosen so that the mathematical expression of the physical laws reflects their inherent symmetries. Already Newton's first law then fixes the time rate ...
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### Why does four-momentum have the same transformation matrix as spacetime coordinates?

I will outline my question in 1+1D for brevity. We can passively transform our coordinate system using a Lorentz boost; $\Lambda^{\bar{\nu}}_{\mu}x^{\mu}=x^{\bar{\nu}}$. I've seen that, by stipulating ...
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### Experiment vs manipulation (Rindler Page-41)

As just another application of the midframe lemma, we end this section with a proof of the obvious-seeming 'reciprocity theorem' which asserts of any pair $S$ and $S'$ of inertial frames, using ...
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### Qualitative analysis of special relativity effects between moving planes (page-38 of Rindler)

Suppose we are in an IF(inertial frame) and a fast air plane flying overhead constitutes a second IF; let it be the top plane in Fig. 2.3(a). Suppose that a flash bulb goes off in the exact middle of ...
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### Could there be some process or event that would make the universe to be Lorentz non-invariant?

As far as we know the universe is invariant under the Lorentz symmetry and does have many other fundamental symmetries from which we derive the fundamental laws of physics. But could there be any ...
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### What does size of an inertial frame mean?

It is the equivalence principle that provides the bridge between the ideal $SR$ model and the real world. According to it, we can find at each event a set of local inertial frames (LIFS), which may be ...
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### Angular-momentum of the Dirac spinor theory

The standard Dirac action $$S = \int d^4 x \bar \psi (i \gamma^\mu \partial_\mu - m) \psi$$ is invariant under Lorentz transformation. In David Tong's lecture note, eq (4.96) lists that the ...
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### Time differential between two signals sent at two different near-relativistic speeds

There is something I don't quite get about relativistic velocities, which I am hoping to clarify with this question. Suppose you have an emitter and receiver both located somewhere far away from one ...
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### For someone staying on Earth, what is the minimum possible time to send a spaceship to Alpha Centauri and have it back?

Suppose we want to send a spaceship to Alpha Centauri and calculate the minimum possible time it will take for us here on Earth to have the spaceship back. We are not interested in how fast the time ...
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### What is the correct derivation for particle concentration from one frame to another?

I. The simplest derivation I can think about is based on conservation of the number of particles and length contraction. In frame S, say we have a volume V (surface S, length l) of particles of ...
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### Units make speed of light dimensionless..?

We shall now adopt a new unit for time, the meter. One meter of time is the time it takes for light to travel one meter ... (page-4, Bernhard Schutz's A first course in relativity) I am confused, how ...
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### Why is some mass converted into energy when neutrons and protons combine to form nucleus?

So some of the mass is converted into energy when neutrons and protons combine to form nucleus. Why? And how? And then why do we need to supply the same amount of energy to separate them?
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### Where/ how does light propagate? [duplicate]

The Michelson–Morley experiment proved there is no aether, but we (used to) know that a wave needs a medium in order to propagate. Einstein showed the invariance of speed but assigned no properties to ...
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### How would a rigid disk rotating near speed of light behave? [duplicate]

Say you had a perfectly rigid disk so that you can't morph it or bend it. If you were to spin near the center of the disk at near speed of light, the edge of disk would have to be faster but of course ...
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### Does this relativistic generalization of the Schrodinger equation make sense? [duplicate]

So I'm aware that the correct relativistic approach to quantum mechanics is through quantum fields, but I'm still interested in the question that follows. We know the Schrodinger equation in free ...
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### Is there a way to assign 4-momentum vectors to spatially extended mass distributions in a covariant manner?

We know that the 4-momentum of a point particle is of the form $p^{\mu} = (E/c, p^{i})$, whose transformations across different inertial reference frames are given by Lorentz transformations. If we ...
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### Why does the trajectory of a relativistic particle "minimises its Minkowski distance"?

The action of a relativistic free particle is $$\mathcal{S}=\int^{t_{1}}_{t_{0}} L dt\tag{1},$$ for $$L=-\frac{mc^{2}}{\gamma}.\tag{2}$$ I understand that a particle will follow the trajectory of ...
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### Vacuum Transitions and Lorentz Symmetry Breaking

There are many "bumblebee" models 1, 2 where Lorentz invariance is violated usually resulting from a local vector or tensor field acquiring a nonzero vacuum expectation value We do not know ...
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### Relativistic doppler redshift

From Wikipedia I can only find "longitudinal" and " closest approach" redshift. I was wondering what resources I can use to find the redshift (and resulting energy change) of ...
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### How does a ring magnet rotating in-place lose K.E. when it does work on an external charge using its curl-free/irrotational/conservative $E$-field?

Consider a ring magnet that is rotating in-place. By rotating in-place, I mean that the ring magnet is symmetrical about an axis and is rotating about that axis. Such a ring magnet produces an ...
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### How to represent a pair of inertial frames in relativity?

Can two Cartesian inertial frames, in general relative motion, be drawn parallel to each other? A picture in Wikipedia suggests this, but some answers on this site appear to differ. Consider observers ...
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### Test for Lorentz invariance of scalar function

This is a simplification of a previous question. I have a function of two 4-vectors and two factors. One factor is on-shell, that is $q_0=\sqrt{M^2+q^2}$. The other factor is off-shell, that is the ...
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### Is there a limit to how close faraway objects can get due to the conservation of angular momentum?

Say a 1kg object is going 1 meter/sec tangentially to a point 600,000,000 meters away, its angular momentum is $$1kg*1m/s*600,000,000 meters$$ If it were to decrease its radius to the point similar to ...
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### Why aren't all photons black holes?

According to Special Relativity, there is no preferred inertial reference frame. And shifting reference frames can cause blue shifting or red shifting of photons. And according to General Relativity, ...
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### Distance contraction and acceleration

I'm trying to understand length contraction. I've created a diagram with three examples. I'm wondering if my diagram is correct. According to this diagram, when you accelerate towards an object, the ...
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### Could the speed of causality be (significantly) faster than $c$?

The other day my son (13) asked me whether it was possible that light went very slightly slower than our best measured $c$, and at the same time had a very tiny mass, but we aren't able to measure ...
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### Can "relativistic mass increase" be explained in terms of time dilation? [duplicate]

If, for example, the body is moving at a speed close to the speed of light, the rest mass will of course remain the same, but many people argue that the relativistic mass increases. But if we take ...
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### Paradox with muons decay [closed]

I wonder what would happen if muons or something similar would travel at 99.999999999% of light speed. Also, can anyone please shine some light on what happens to the sunlight (photons) and the ...
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### Relativistic angular momentum confusing definition

After reading Wikipedia, I'm confused by the relativistic angular momentum definition. OK for the 4-angular momentum tensor. But does it mean that the following more intuitive "angular momentum&...
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### A synchronous clock problem in a rigid frame with constant proper acceleration

I am a beginner of general relativity. I read and follow the notation in Andrew Steane's book, Relativity Made Relatively Easy, chap 9.2. Suppose there is an rigid accelerating frame with constant ...
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In the Minkowski 4-dimensional space-time $(\mathbb{M}^4,\eta)$ the dot product is: $a\cdot b = -a^0b^0 + a^1b^1 + a^2b^2 + a^3b^3 ~\qquad~ a = (a^0,a^1,a^2,a^3) ~~,~~ b = (b^0,b^1,b^2,b^3)$ Now ...