New answers tagged

1

If you put a clock in a centrifuge, the clock will indeed slow down (relative to the lab frame) by a factor of $\gamma$, just as you derived. Experiments in particle acclerators confirm this. And yes, $v = \omega r$ must be less than $c$: you can not physically spin an object faster than $c$ (your centrifuge or similar apparatus would fail long before it ...


3

As pointed out in another answer: in the case of macroscopic objects there is the practical problem that a force large enough to cause close-to-instantaneous acceleration to the speed of light will disintegrate that object. Sub-atomic particles such as Muons are not subject to such a limitation. There is the 1963 'Measurement of the Relativistic Time ...


2

Yes you can get there in a short time as far as your own aging goes, but maybe not seconds because your body can only withstand some modest amount of acceleration. If one could somehow accelerate the whole body at once, without compressing or altering the blood pressure, or otherwise allow it to withstand large accelerations, then the time overall could be ...


-1

Yes this is a common confusion among "high schoolers" and not only and initially seems as a paradox from our everyday experience with relative moving objects. The problem goes away if you understand that light is not an object but a wave. To answer with a paradigm as simply as I can, lets consider the following question and scenario which covers ...


0

given that light always travels in a vacuum at a fixed speed, could all other motion be measured against this to give a real value to the motion of all objects ? No. Even though light in a vacuum always travels at the same speed in any inertial frame, the velocity of anything traveling at a speed other than light-speed will be be different in different ...


1

A photon always moves at the speed of light $c$, so one can never be in the same frame of reference. What causes the speed of light to be slower in a medium is the interaction with this medium. This is explained in more detail here: As the wave moves through a medium, it intersects with (usually) the electrons, causing them to vibrate. That vibration does ...


2

Your setup is different from the "superluminal" astronomical jets. The events in the astronomical jets that seem to be spacelike (faster-than-light) separated are actually timelike (slower-than-light) separated, and in fact are causally connected. They only seem to be spacelike separated if one mistakenly assumes that they're the same distance away....


2

The dielectric constant is a function of frequency. The value of 80 is for DC regime (zero frequency). You need the dielectric constant at the frequency of visible light if you want to find the index of refraction for visible light. You can see how the dielectric constant drops with increasing frequency in this figure. The frequency of visible light is ...


-2

Einstein was already aware of this. As can be seen and heard in the video. But I don't know what Einstein has to say about observing the universe on both sides of the Earth. If we look at the northern hemisphere and then at an opposite point in the southern hemisphere, we should see something very different if the velocities of the photons coming from these ...


2

Of course you can measure the one way speed of light, the only "gotcha" is that you need to use two different clocks in different places to do so. So you need to define how to synchronize them. For example, you could synchronize the clocks in the same place, then carry them slowly and carefully equal distances to the final test locations, do the ...


7

If the speed of light is kc in a direction where $k\in[\frac{1}{2},1]$, then what would the speed of light be in the opposite direction? This can be found out by just figuring out what the speed of light must be in the opposite direction to ensure that the average speed of light across the total journey is $c$. So, if we have the speed during 1st half as $k$...


2

Two observers at rest relative to one another (as Proxima Centauri and the Earth are assumed to be for the purposes of the blog post you referenced) certainly can keep their clocks synchronized. For example, if they are 4 light years apart and Earth sends a radio message that says "it is now noon on January 1, 2100" then when the receiver gets the ...


1

Perhaps this question is answerable in a purely classical electromagnetic wave setting. You need to be aware that there are different definitions of "speed" for waves. The speed of light is a "phase velocity", which is not really a velocity (see below). The phase velocity is more the ratio between frequency and wavelength. Both are ...


4

You are confusing photons with electromagnetic waves, light. They slow down to 225,000,000 m/s in water with a refractive idex of 1.3, to 200,000,000 m/s in glass and to 125,000,000 m/s in diamond. So its speed can be varied with variations in the medium. This is not correct . Light,the electromagnetic wave, slows down. Light is made out by the ...


1

You need to account for energy. Accelerating atom to the speed of light means infinite energy. Spaceship just collapsed into a black hole. Accelerating atom to a large percent of the speed of light means energy came from somewhere. Lets assume energy was stored in the same atom. Then as you increase the speed, you need more and more energy to be wasted on ...


2

The atom will not travel at the speed of light. Period. IF it travels at the speed of light, the laws of physics have been violated, in which case, why would you expect other laws to hold? So no, it cannot.


3

We exist along wordlines in 4D space. We like to measure three of those dimensions using one unit and the fourth using another, but we could use the same unit for all four and the constant $c$ would vanish from all calculations. We would then notice, for example, that nothing other than light can include both (0, 0, 0, 0) and (1, 0, 0, 1) in its wordline (in ...


6

First: From a practical standpoint, it is not exactly correct to say that we use the speed of light to define the value of the meter, or the value of a second. Rather, we should say that we used specific measurements of the speed of light, taken by specific scientists at specific places and times, to define these units. Suppose, for the sake of argument, ...


2

You actually describe, why the speed of light is necessarily assumed to be the fundamental constant with the definitions you mention. Although of course its actual numerical value in the end depends on OUR choice of definition (for example on which part of the distance traveled by light in one second defines a $m$.). Let's use an analogy: Let's assume the ...


9

The numerical value of the speed of light is not a universal constant. It's the quantity that is a universal constant. As an analogy, in Newtonian physics, the distance between any two points in space, or the time interval between any two events, is a universal constant. Pick any two points in space in a Newtonian universe. Say, one observer measures the ...


1

the velocity of that photon along that axis would have to be some fraction of infinity This is not correct. The projection of a vector onto an axis is some fraction of the actual length of that vector. It is not some fraction of the hypothetical length that the vector would be if it were pointing in a different direction. The operation you describe is not ...


0

There are experiments done using stellar aberration which can measure the speed of light using light that only travels in one direction, basically rules out the loop hole you are attempting to use. In addition if light did travel at different speeds in different directions then you would break special relativity/Lorentz symmetry. Breaking these symmetries ...


1

The idea of the speed of light being infinite one one direction and finite in another is nonsense. However, to take your question at face value, if any beam of light always had two components of velocity, one infinite and the other finite, then it would be impossible to direct a beam of light at any arbitrary point on a sphere around its source, since the ...


0

To remove added complication from the problem. consider a front surface mirror, silver coating on the front. Maxwell wave theory simplifies the problem. A plane wave impinging on the metal surface, induces a current into the surface, the induced current then re radiates, the magnetic field component of the incident wave is parallel to the reflected wave ...


2

The velocities in cosmology that can exceed $c$ don't have much in common with the velocities in special relativity that can't. Even in special relativity, if you define a "recessional speed" similar to the way it's defined in cosmology, it can exceed $c$ even though the usual special-relativistic relative speed of the same objects is less than $c$....


2

entanglement between two qubits means that if a measurement is made on one of them, the other one is decided instantaneously. This is true, but this does not allow for faster than light communication. If you have one qubit with you and i have one qubit with me and you make a measurement on your qubit, that will mean my qubit is decided . But how does that ...


3

So how can we calculate the speed of light for different frequency? It depends on how much prior information you want to require of your calculation. In the simplest case you may just look up an approximate formula for the speed of light in your medium of choice as a function of wavelength or (less common) frequency. Of course, this relies on somebody ...


3

This question can be reformulated as: “Does the index of refraction of a given medium depend on wavelength” (inverse of frequency), the answer is given by Cauchy’s formula: https://en.wikipedia.org/wiki/Refractive_index


0

Phase velocity is defined as how the front of a constant phase is moving in space when time changes. Therefore, for $\phi(x,t) = \phi_o$, a constant. Under this condition: $$ v_p = \frac{dx}{dt}\vert_{\phi_0}. $$ Therefore, in your ⓑ the $$ \frac{d\phi}{dt} = 0. $$


2

Good question. Interacting systems move in the direction of thermal equilibrium. At thermal equilibrium particles satisfy Maxwell–Boltzmann distribution, and their mean kinetic energy is the same and proportional to the temperature. Speed of a particle is a function of the kinetic energy $E$, and in special relativity can be expressed by a formula $$ v=\sqrt{...


0

The speed of light is 299 792 458 meters per second, so in 1 nano second, light travels about 30 centimetres. So with a led and a frequency emitter generating a 0.5 10-9 square we can detect on the other side of the bench with a photo sensor the fall of the signal and adapt the distance until it would be in phase with the emitter and we can measure +-30 cm ...


2

If you managed to build your scissorgun in real life then you would have something, but as a mere thought experiment, the resolution is simple: your assumptions are logically inconsistent. At each $x$ along the closing scissors you have to push the cart from $x$ to $x+dx$ in a time less than $dx/c$, and that simply can't be done. If you push at separated ...


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