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1

There is no paradox. The question you pose is exactly analogous to this: Two presidents must sign a treaty at 6pm or a bomb will go off. They sign it at 6PM London time, so the bomb doesn't go off. But in New York it appears that they have signed it at 1PM, so the bomb does go off. How can this be? An event cannot be at the same time in two different time ...


4

The exact number depends on the cosmological model and its parameters. In special relativistic models (e.g. the Milne model), the redshift at the speed of light is of course infinite. However, in all viable cosmological models, recession velocities exceed the speed of light for objects with redshifts greater than $z\sim 1.5$. The general relativistic ...


1

SPEED of light is completely independent of the Wavelength. Provided, The Medium is Vacuum or Air.. But In other Medium ,like Water/Glass the Speed Of Light of Different Wave length decrease differently and This Phenomenon is Known As Dispersion Of Light In a medium the Speed Of RED Light is Maximum and that of Violet is Minimum. This Is How We See 🌈 ...


1

Imagine that you have a great big loudspeaker on top of a mountain, with a switch that makes the loudspeaker cone jump into one of two positions. When you flick the switch down, the cone jumps forwards and sends out a positive pulse, and when you flick it up, the cone jumps back again and sends out a negative pulse. The speed at which your standard pulses ...


3

The speed of light is always c in vacuum, when measured locally, independent of the wavelength. Though, in a medium, the index of refraction is n=c/v. Speed of different em radiation in a medium Now if the index depends on the wavelength, then different wavelength (color) light has to have different speeds in the medium. In optics, the refractive index ...


1

No, they are related by the formula $$c = f \cdot \lambda$$ with speed of light $c$, frequency $f$ and wavelength $\lambda$. A change in frequency demands an anti proportional change in wavelength and vice versa, since the speed is constant. It is not possible to change the frequency and leave the wavelength constant. This is quite intuitive because the ...


1

The speed of a wave is given by: $$c=f\lambda$$ Where $c$ is the speed of the wave, $f$ is the frequency and $\lambda$ is the wavelength. You're right that different colours have different frequencies, but light with a lower frequency has a longer wavelength, in other words if $\lambda$ goes up then $f$ has to come down so they cancel each other out and ...


0

It's not enough to say that the bomb will blow up if the two presidents don't sign the agreement simultaneously. You have to define how the bomb will decide whether or not the signing is reckoned to be simultaneous or not. How is it wired? It is wired to compensate for time delays? If so, are the supposed time delays calculated by assuming that the speed of ...


0

In particle physics there exists the standard model, which is an encapsulation of an enormous amount of measurements and observations , and in addition its predictions are successful. This model is based on both quantum mechanics and special relativity. In special relativity nothing goes faster than light. The whole edifice would be broken if the particles ...


2

"I'm sorry, officer. There's no way I could have been going that fast. You see, my speedometer only goes up to 85mph." Yeah. That doesn't work too well with the police. It doesn't work all that well in physics either. It would be an enormous ethical quagmire for the entire scientific community to try to claim nothing travels faster than light when ...


2

The real problem is that the trigger on the bomb is ill specified. It's not as complete as you might think. The entire point of these simultaneity exercises is to demonstrate that simultaneity is not preserved between frames of reference. It's an odd artifact of relativity, and that's why it needs thought experiments like these. Thus, a physical bomb ...


-1

The answer lies in the question itself. The bomb does not explode because the simultaneity is considered only from the reference of the train. This is similar to the limo in the garage question in Leonard Susskind's Theoretical Minimum:Special Relativity. What I mean is that the bomb explodes only if the two light beams don't reach to the detector at the ...


1

If the bomb, the laser, the sensors, and the presidents are all in the same frame of reference, it will not matter what other frames of references see the laser do.


3

Here's an even more alarming paradox: I'm about to flip a coin. Next to me there is a bomb with two properties: 1) The bomb blows up if and only if the coin comes up heads. AND 2) The bomb blows up if and only if the coin comes up tails. Whoa! The bomb either has to blow up or it doesn't, and either way we have a paradox, right? What is the ...


1

It takes the spaceship 4 years to get there, and then it takes light from the spaceship getting there 4 years to get back, i.e. 8 years for an observer on Earth to see it land on the planet.


0

It all depends on what the meaning of the word "appear" is. In about eight years, you'll see the ship land, and you'll say "Ah. I see the ship landing at a place four light years away, so it must have landed four years ago". Does "appear" refer to what you see, or to the meaning you attribute to what you see after you've made the necessary corrections? ...


1

Will it appear as if the trip took 8 years to complete? Yes.


0

There is a famous (but wrong) explanation, why you can never go from $A_0$ to $B$. It goes as follows: In order to reach $B$ you first have to reach the mid-point between $A_0$ and $B$. Let's call this mid-point $A_1$ and let's assume, that you need the time $T_1$ to reach this mid-point. Next, let's assume, that you have reached the mid-point $A_1$. ...


0

There is no maximum speed. You can approach $c$ arbitrarily closely, but since you cannot reach it it is an asymptotic limit rather than a maximum.


0

There is a maximum speed, but you haven't given enough information to calculate it. If you go fast enough, then the relativistically beamed and boosted cosmic microwave background could become a significant source of radiation pressure (that opposes any accelerating thrust) and heating, which you either have to reflect or deal with in some way. Secondly, ...


2

Your desk is already moving at 99% of the speed of light, in an appropriately chosen frame of reference. Your desk is already moving at 99.9999999% of the speed of light, in an appropriately chosen frame of reference. That sentence remains true if you put in any number less than 100.


0

In theory, a spaceship could travel infinitely close to the speed of light without reaching it. This would require a near infinite force, however. As you come closer to the speed of light, you become more massive. A greater force is necessary to push a greater mass. As you go infinitely close, you require an almost infinite force. At the speed of light, and ...


1

Suppose you're in Chicago, facing New York, which is 800 miles straight ahead. Now turn ninety degrees to the right. All of a sudden, New York is 800 miles to your left! How did New York manage to shift its position so dramatically all of a sudden? The answer, of course, is that it didn't. What changed is your description of New York's location, which ...


3

The object does not physically shrink. Its length appears to change when viewed from a moving reference frame. You must remember that the effects of relativity are symmetrical. If a fast moving spaceship, and all the people in it, seem to have contracted in length from your perspective, from their's it is you who is fast moving and contracted. The effect ...


-6

It's just a math model, it's not necessarily literally describing reality. You can interprete it that way in some instances if you want to. I don't think that any of the special relativity effects have been observed directly and explicitly..


1

It shrinks for simultaneous (according to your own clock) readings of a your meter stick at both ends. Given that the object is in a different frame, the measurement cannot be simultaneous to it's clock, and will furthermore be of a not contracted length. So you have a "shorter" time displacement and you should have as a consequence a shorter spatial ...


0

I disagree with those who dismiss this question. As Ben Crowell reminds us- Einstein himself considered it. One aspect of relativity that is often overlooked is its reciprocity. If you are moving relative to me then any relativistic effects that apply to you from my perspective (eg the slowing of your clock), apply equally to me from your perspective. The ...


0

I do not agree with David and I found his answer kind of odd. For simplicity let us assume we work in $(1,-1,-1,-1)$ Minkowski space. The photon is travelling in direction along $x$-axis. At time $0$ the photon is at point $(0,0,0,0)$, and at time $1$ at point $(1,c,0,0)$. Thus the space-time distance of the two events are $$ c^2-(c-0)^2=0 $$ As a ...


-5

The laws of electromagnetism, which at the most fundamental level are four equations, are the classical laws that govern light, or electromagnetic waves. i.e. light depends on a fundamental force of nature Maxwell equations $$\nabla\cdot E=\frac{\rho}{\epsilon_o}$$ $$\nabla × E=- \frac{\partial B}{\partial t}$$ $$\nabla\cdot B=0$$ $$\nabla × B= \mu_o j+\...


0

The cutter has to move at relativistic speeds too. From the perspective of the dough: The descending cutting edge appears slanted, with the front of the 'circle' cut before the back. During its acceleration the cutter's shape warps from the front to slant the other way After the acceleration the front retracts before the back. The process takes a finite ...


6

The speed of light is a dimensionful constant and, as such, it is impossible to talk about changes to the speed of light without being dead clear about what you do want to keep constant. Your question doesn't really give any meaningful benchmarks for this, so to some extent your question is completely unanswerable. On the other hand, your emphasis on what ...


1

Photons are elementary particles, massless, they always travel at speed c in vacuum, when measured locally. Though, you are correct, light can slow down in media, but what actually slows down in media is the wavefront. You are asking whether between atoms light travels at speed c or not. Individual photons still travel at speed c in vacuum, inbetween the ...


1

Are we all travelling in the speed of light? No, for the simple reason that, in accord with the Lorentz transformation, any entity with speed $c$ in an inertial reference frame has speed $c$ in all inertial reference frames (for simplicity, I assume the context of the Special Theory of Relativity). That is to say, the fact that you have a rest frame, the ...


2

When you ask whether we are travelling at a certain speed, you must answer the question 'relative to what?'. Relative to my desk I am not travelling. Relative to a car passing on the street I am travelling at 30mph. Relative to some other star in the Milky Way I may be travelling at thousands of mph. Relative to a proton in the Large Hadron Collider I may be ...


1

Light’s velocity in a medium changes compared with its velocity in vacuum because the electrons in the atoms of the medium experience forces due to the light passing through, and, as they are accelerated, radiate light of their own which superposes with the incoming light. (Showing that this additional radiated light changes the phase velocity of the ...


1

Yes everything you look at happened in the past. The speed of light in a vacuum is 299,792,458 meters per second. It travels slightly slower in materials according to their refractive index. When you look at the moon, you see it as it was about 1.3 seconds ago, the Sun from about 8.3 minutes ago, even from your window to your front yard takes a few ...


1

Yes the speed of light is slow and everything you see happened in the past.


15

For clarity of thought in the physics of distance, time and motion, one should be careful with words such as "moving", especially when people speak of "moving through time". The trouble is that this creates a confusion of two meanings of the word "moving". There is physical motion, when bodies have relative motion and two different worldlines have different ...


0

The answer to your question seems to be agreed as yes with one small proviso. Observers in different inertial frames, who are also moving forward (for them) at speed c are moving in a different direction from yours in four dimensions. Equivalently, your moving forward in your inertial frame is at an angle to theirs. The small proviso is your use of the ...


0

One way to describe Special Relativity in terms of first principles is There are two different types of dimension. All directions of the same type are equivalent. From this you find that the distance formula is defined by the equation $$D^2=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2+(z_2-z_1)^2-(w_2-w_1)^2}$$ with $D$ being the spacetime distance. So the distance ...


5

You are correct, the four vector (velocity) is defined as a four vector in four dimensional spacetime, that represents the relativistic counterpart of velocity (3D). Physical events correspond to mathematical points in time and space, the set of all of them together forming a mathematical model of physical four-dimensional spacetime. The history of an ...


11

As Lewis Carroll Epstein explains in Chapter $5$ “The Myth” of his excellent book Relativity Visualized: There is afoot an errorneous idea. It is that in physics the ultimate reality is a mathematical prescription, an equation. In fact, the ultimate reality is a little story or myth. Then he divided myths into $2$ categories: good and bad ones. Good ...


24

You, referring to yourself, always have a 4-velocity: $$ u_{\mu} = (c, \vec 0) $$ which has: $$ u_0 = c $$ Hence, moving through the time-direction at the speed of light. You can't move through space (otherwise, there would be a preferred frame in which you were not moving through space). A moving observer that sees you moving through his definition of ...


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