# Tag Info

7

One way to think of a "moving shadow" is by following the last photon that was allowed through. In that case, the speed of a shadow is exactly the speed of light. On the other hand, you could also define the speed of a shadow as the speed of the boundary between dark and light. In that case there is no thing that's actually moving, so there's no bound on ...

4

in relation to anything else that can make such measurements. As the speed of light is universal, nothing can see any other massive field moving at the speed of light (which is reserved for massless fields) your 0.51 number suggests that you expect that naive addition of velocities holds when velocities approach the speed of light. This is wrong. Here is ...

4

Firstly: *in a vaccuum *inertial Einstein's Special Theory of relativity postulates that the speed of light in a vacuum is same for all inertial frames. suppose a neutrino is there moving at the speed of light For a neutrino to move at $c$, it has to be a massless particle. We're not sure of that yet. Apparently the existence of neutrino ...

3

Photons don't have mass, but they do have energy and momentum. And since they can be absorbed or reflected, they can transfer their momentum to whatever it is that reflects or absorbs. The amount of energy is proportional to the frequency $\nu$ of the light: $E = h\, \nu$, where $h$ is Planck's constant. The momentum is $p = h\, nu / c$, in whatever ...

3

You seem to have misunderstood some things about the work of Kenneth Nordtvedt (spelled that way, not Nordvedt). He is mainly known for pointing out that in some well-motivated alternative theories of gravity (i.e., not general relativity), the equivalence principle could be violated. Massive, self-gravitating bodies would have slightly anomalous ratios of ...

3

So let's say the rocket has a camera that's supposed to take a frame every $1/30$-th of a second. From the earth's point of view, this frequency will be reduced (by how much exactly is left for you as an exercise). Let's just for the sake of simplicity say that on earth it looks like the camera takes just one frame every (earth-)second. Next comes the ...

2

This is essentially the same as lurscher's answer, but from a different perspective. Special Relativity is often thought of as some kind of mystical force that acts on objects and stops them moving faster than light. This misconception is the reason for questions like this one. Special Relativity is actually just a prescription for telling us what events in ...

2

It is not physically possible to accelerate any object with mass to the speed of light using magnets. There are a few reasons for this. First, it is a widely held belief that it is impossible for anything with mass to achieve light speed period; that it would take an infinite amount of energy to accomplish this and there is slightly less energy than that in ...

2

Rather than looking at one orbit of Io, consider observing Io and Jupiter for around 200 days, starting when the Earth is exactly between the Sun and Jupiter, and ending when the Earth is opposite Jupiter, with the Sun in between. In the 200 days, Io will make around 110 orbits of Jupiter. But, importantly, the light from that last orbit of Io will need to ...

2

No, because the uncertainty principle operates between position and momentum rather than position and velocity. For speeds much less than $c$, momentum is just proportional to velocity: $p = mv$. But at relativistic speeds we have to use the relativistic version, $$p = \gamma mv,$$ where $\gamma = 1/\sqrt{1-v^2/c^2}$. Substituting this in and squaring both ...

2

Early in the universe the expansion rate was much greater than it is today, which is a way of saying that spacetime was strongly curved. You really need general relativity to properly work out what happens, but a good way to think about it is that by the time a light ray gets from A to where B was, the expansion of the universe has carried B even further ...

2

In the context of Special Relativity, the speed c is both an invariant and a constant. As in invariant speed, some object with a speed c in an inertial frame of reference has the same speed c in any inertial frame of reference. As a constant, the speed c is the conversion factor from temporal units to spatial units, i.e., one second (a measure of time) to ...

2

We are free to define our units however we wish. These are examples where the units are essentially determined by the magnitudes of the constants from certain historically important equations. The simplest example here is the speed of light in vacuum. Its value is defined as $299\,792\,458$ meters per second. Now, the second is already defined with ...

2

Calculate the spacetime interval $$\Delta s^2 = -c^2\Delta t^2 + \Delta x^2 + \Delta y^2 + \Delta z^2\text{.}$$ In this sign convention, $$\begin{cases} \Delta s^2 < 0\text{,}& \mbox{timelike separation}\\ \Delta s^2 = 0\text{,}& \mbox{lightlike separation}\\ \Delta s^2 > 0\text{,}& \mbox{spacelike separation}\\ \end{cases}$$ Someone ...

2

The speed of light is entirely a local concept - it does not care if there are 10 atoms or 10 billion galaxies somewhere in the Universe. Obviously we can't go to distant galaxies to directly measure the speed of light, so in the absolutely strictest sense this is not directly empirically tested. However, the constancy of the speed of light is one of the ...

1

For (1), the event $a'$ is co-located in time, i.e., simultaneous with event $a$ and thus the associated interval is space-like (the distance through space is greater than the distance through time in any frame). There is no world line (time-like curve) that includes the events $a$ and $a'$ so, the event $a'$ cannot be the event "receive signal initiated at ...

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Does the expansion of the universe soon after the Big Bang affect the amount of time that light takes to reach us? The time light has had to travel is simply by the age of the universe (or slightly less, because the very early universe was opaque). The age of the universe is 14 billion years, so that's how long the most ancient light has had to ...

1

There are a whole bunch of misconceptions here so I will try to address them one by one. "Light particles" (photons) don't have a physical size in the classic sense of the term. They aren't tiny spheres flying through space really fast. See How is the size of the particles is determined? If your body were shrunk to to a very tiny size on the order of a ...

1

What causes these constants to have the values they do is simply our choice of a system of units. When you have a unitless constant, it makes sense to ask why it has the value it does. For example, two of the lines in the visible spectrum of hydrogen have wavelengths in the exact integer proportion of 28/25. When this was first discovered, it made sense to ...

1

Nice question. I don't understand the Lorentz-violating possibilities very well, so I'll only try to comment on Lorentz-invariant theories. The classic papers are Tolman 1917, Bilaniuk 1962, and Bilaniuk 1969. Bilaniuk 1969 can easily be found online by googling, and gives a good overview. Tolman proposed a causality paradox involving tachyons, known as ...

1

No. First of all, Planck's constant is not a speed, so you can't compute $c - \hbar$. But you can reword the question to get around that problem, something like this: Is there some speed $\epsilon$ such that an object traveling at speed $c - \epsilon$ could experience a quantum fluctuation that temporarily takes its speed to greater than $c$? The ...

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This kind of question has a long and honorable history. As a young student, Einstein tried to imagine what an electromagnetic wave would look like from the point of view of a motorcyclist riding alongside it. But we now know, thanks to Einstein himself, that it really doesn't make sense to talk about such observers. The most straightforward argument is ...

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There is no changing gravitational field. The solar gravitational potential through which the Earth moves has been set up a long time ago and continues to be present as the Earth moves through it. Consequently, there is no dependence on the time lag--this is just the same as why you don't need to worry about retarded potentials when deriving the energy ...

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We did this experiment in my undergraduate physics class. Search for "Michelson-Morley experiment classroom" and you will find products such as this: http://i-fiberoptics.com/laser_detail.php?id=2120 Before the advent of lasers with a visible beam, the alignment of interferometer components was very difficult to achieve under ordinary laboratory ...

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