# Tag Info

25

As far as I know, the only clue at the time that the speed of light would be invariant were Maxwell's Equations where "something" shows up as a constant. However, speed of light being invariant in all inertial reference frames is very counter-intuitive. One might rather expect physics to be slightly different in different frames, which is what the MM ...

19

It was a completely unexpected result at the time. The principle of the MM experiment hinged on the hypothesis that Maxwell's equations of electromagnetism were valid only in a special frame of reference called the aether frame.The speed of light was equal to its standard value only in this frame and its speed in any other inertial frame had to be given by ...

14

The famous equation $E = mc^2$ is actually just a special case of the relativistic equation for the total energy: $$E^2 = p^2c^2 + m^2c^4 \tag{1}$$ where $p$ is the relativistic momentum and $m$ is the (constant) rest mass: $$p = \frac{mv}{\sqrt{1 - v^2/c^2}}$$ For an object that isn't moving $p=0$ and equation (1) becomes: $$E = mc^2$$ which is ...

13

As far as I know the first time anyone proved that light has a finite speed was when the astronomer Rømer discovered variations in the timings in the transits of Jupiter's moons. He correctly attributed this to the time light took to reach Earth from Jupiter. His calculated value for $c$ was about 26% too low, but that was pretty good given the state of the ...

8

There were a couple of clues that Einstein and others found that led to the conclusion that the speed of light was special. First, using Maxwell's equations, you can derive the existence of electromagnetic waves that travel at $$c = \frac{1}{\sqrt{\mu_o\epsilon_0}} \approx 300,000\, \textrm{km/sec}$$ where $\mu_0$ and $\epsilon_0$ are constants you can ...

9

does this equation mean masses are just condensed energy? No, it means that mass is just another form of energy, just like heat, motion, electric attraction, etc. For example, the energy of a charged sphere is $$E=\frac{3}{5}\frac{Q^2}{R}$$ This equation doesn't mean that charge is just condensed energy; it means that charged objects have energy. ...

5

Within the theory of special relativity this is postulated. Hence the theory does not address why this is true. If you're wondering why special relativity postulates this, the simple answer is that these are arguably the simplest postulates that give a theory that explains observed phenomena. You may want to read about the history of special relativity to ...

5

Yes, this statement is true, in the sense that the four-velocity $u^\mu = (\gamma, \gamma \vec{v})$ always satisfies $$u^\mu u_\mu = 1$$ as you can check using the definition of $\gamma$. (I'm setting $c=1$.) Therefore the magnitude of the four-velocity is always equal to the speed of light. However, this statement can be really misleading. It's true that ...

3

Yes, this does happen. Cherenkov radiation is a well known effect. It produces that blue glow you might have seen in pictures of nuclear reactors resulting from electrons passing through water a speeds faster than light.

3

I want an answer which is free of mathematical relations.I want an insight rather than a mathematical relation. Very well. Do you see?

3

Yeah, @EddyKhemiri, as @almagest wrote it isn't just visible light, but rather that all electromagnetic waves moving through a vacuum travel at $c$. Also- just a pet peeve, but remember that this is the speed in a vacuum; it can be slower in different mediums.

3

The link given by LLlAMnYP for the Ehrenfest paradox gives the classical physics rational : Any rigid object made from real materials that is rotating with a transverse velocity close to the speed of sound in the material must exceed the point of rupture due to centrifugal force, because centrifugal pressure can not exceed the shear modulus of ...

2

No, they don't disprove it. However the Alcubierre metric, which underlies the warp drive stuff, requires something people refer to as 'exotic matter' which in this case means matter with negative energy density. Such matter violates many assumptions, and would normally be considered not to be possible (indeed my memory of Alcubierre's original paper is ...

2

The speed of light was first measured by Ole Christensen Rømer (Danish pronunciation: [ˈo(ː)lə ˈʁœːˀmɐ]; 25 September 1644 – 19 September 1710) was a Danish astronomer who in 1676 made the first quantitative measurements of the speed of light. When Maxwell formed what is the classical electromagnetic theory it was evident that the speed of light would ...

2

I'm not 100% sure of your level so just as a heads up, I put some comments in parentheses that are meant to give technical caveats. If they don't make sense just ignore everything in parentheses, the zeroth order answer You can look at it that way, but actually it turns out to be much more complicated to understand what's going on in detail. (Basically you ...

2

Special relativity does not tell you, that there are inertial systems moving along with a light ray. The formula for velocity addition is essentially a formula about transformation of a velocity in the frame of a moving observer. It's just not the right question to ask, what an observer moving at $c$ would observe. Since there are none.

1

The velocity addition formula applies when there are two observers (say A and B) moving with respect to each other. If C is some other object, we have three relevant velocities: That of B as measured by A, that of C as measured by B, and that of C as measured by A. But in your setup there is only one observer. (A light beam is not an observer; it has no ...

1

Correct; in general the speed of light is constant only as measured by local inertial observers. As an extreme example, consider a photon emitted from a galaxy far, far away, in our direction. Although it moves away from the galaxy in the direction of the Milky Way, the expansion of space makes it increase its distance from us. Eventually, however, it will ...

1

Actually, it's NOT true that in SR the speed of light in vacuum is the same for all observers, regardless of the motion of the light source. This is true only for inertial observers. The same applies for GR, in which the generalization is a "freely falling frame" (a local inertial frame without effects of gravity). A good reference: Speed of Light

1

Yes, but by definition. Not by any meaningful physics. Imagine a path through 3-space. You can define the path by a function of time that returns a position. ${\bf f}(t)=(x(t),y(t),z(t))$. Then the velocity as a function of time is ${\bf v}(t)={\bf f}'(t)$. Easy. You could do the same thing through 4-space, by describing a path parameterized by some other ...

1

The time dilation relative to a stationary observer is given by: $$\frac{d\tau}{dt} = \sqrt{1 - \frac{v^2}{c^2}}$$ where $d\tau/dt$ is the ratio of the elapsed time on the moving object to the elapsed time for the stationary observer. For any value of $v$ greater than zero the ratio $d\tau/dt \lt 1$ meaning there is some time dilation though in practice ...

1

What you are referring to is a special case of the Ehrenfest Paradox In its original formulation as presented by Paul Ehrenfest 1909 in relation to the concept of Born rigidity within special relativity,1 it discusses an ideally rigid cylinder that is made to rotate about its axis of symmetry. The radius R as seen in the laboratory frame is ...

1

Any two points in spacetime are linked by a four-vector that physicists conventionally write as $(x^0, x^1, x^2, x^3)$, where $x^0$ is normally the timelike dimension and the other three components are spatial. If we use the usual Cartesian coordinates in flat spacetime we'd generally write the four-vector as $(t, x, y, z)$. In this case suppose the light ...

1

As per the comments, I wasn't taking into account the relativistic addition of velocities, which is becomes relevant when designing scenarios with such high velocities. So for a observer in the point specified in my argument, the fastest objects (object #1 million, object #999.999, ...) would appear to have velocities close to light speed, but they would ...

1

One argument goes as follows: Maxwell's equations predict many things, but you can massage them into a form exactly like an equation that describes a broad variety of waves. Call this "the wave equation". So imagine you have a container of water and you generate ripples. You could move your head and travel along with one ripple, so that from your point of ...

1

I will try to answer this question with my basic understanding of special relativity: Is matter condensed energy? It kind of is, but a better way to phrase it would be that everything that has energy, (behaves like it) has mass. Imagine you have a hollow box with the insides covered with perfect mirrors and you put it on a scale. If you shone a light ...

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