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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

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. ...

12

Not really. The "speed of light" has very little to do with light; it is built into the actual geometry of spacetime independent of what matter fills it. In particular, $\epsilon_0$ and $\mu_0$ don't tell us anything physical about the vacuum; looking at the (simplified) expressions E = \frac{1}{4\pi \epsilon_0} \frac{q}{r^2}, \quad B = ...

7

If you pay careful attention your notice that cosmic ray passing the earth just now. You are moving at 99.999%$c$ relative that particle. In fact the whole planet is doing so. From which we conclude that you don't even need a lot of money to make people go close to $c$, you just need the appropriate frame of reference. Now, I know perfectly well that that ...

4

You misunderstand special relativity. For objects that are moving at large speeds, the time runs more slowly for the object compared to the observer who measured the speed. To observe the motion of the object, you don't have to go to its coordinate frame and observe from there. You observe from the outside, that's how you measured the speed in the first ...

4

A better way to think of it is "speed of causality". That's the fastest any cause-and-effect will spread over space. With nothing to cause it to go slower, changes to electric and magnetic fields will occur at that speed. No coincidence that changes to spacetime (causing gravity) propigate at the same speed. You really need to show how Minkowski spacetime ...

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 ...

3

The basic idea is that physical laws are same in all inertial frames. Framing your question in a different way: Why do we generalize a formula(which gives time-dilation) whose derivation is based on a light clock to physical clocks and even the biological clock? A very interesting argument was given by Feynman in his Lectures on Physics, Vol:1. ""To ...

2

Given the context of the question, the fact that it seems to be about $E=mc^2$ specifically, and that the OP says he's having a hard time understanding it, i'm going to try and give a simple answer in plain english without a load more complicated formulae. I am no physicist, and although the concept may not be that easy, the formula is pretty simple, maybe ...

2

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 ...

2

Nonsense. Maxwell derived his electromagnetic equations, with $\epsilon_0$ and $\mu_0$, and those quantities were known. The fact that his equations led to the speed of electromagnetic waves to be, in terms of $\epsilon_0$ and $\mu_0$, equal to the approximately then known speed of light is a big part of what led Maxwell to conclude that light is ...

2

Let me explain light. Classically, light is electromagnetic radiation. There exists a field permeating all of spacetime called the electromagnetic field. Charges create curvature in this field. When charges accelerate, waves are created in this field. These waves are what we perceive as light. A little more specifically, let us examine Maxwell's equations ...

2

If I'm reading the question (v1) right, you present a paradox in paragraph 2 (commonly called Bell's spaceship paradox) and then try to resolve it in the next few paragraphs. Your resolution doesn't make sense, as pointed out in the comments. The mistake is that $u_2'$ is not zero, by the relativity of simultaneity: different observers will disagree on the ...

2

You have this backwards. What you state, the fact that "time is relative", is a consequence of the theory rather than a cause. Assume some light ray travels some distance in reference frame 1 and is seen also from reference frame 2. The trajectory is obviously different in both frames. That's nothing special that Einstein would have introduced : just try ...

1

Reichenbach's original volume, "Axiomatization of the Theory of Relativity", appeared in 1924. It is one of a long string of works that periodically rediscover and/or explore the issue of non-Einstein synchronization in Special Relativity. See for instance this review on "Synchronization Gauges and the Principles of Special Relativity" and refs. therein ...

1

There are some materials, called Birefringent in which the index of refraction depends on the direction in which light is moving (often also dependence on the particular polarization of the light). This is due to the crystallin structure of the material which allows faster propagation in one direction or another. Another example would be a magnetized ...

1

Science does not say that the speed of light is constant. Rather, a lot of people with fancy clocks and tape measures have expended a lot of effort measuring the speed of light and have discovered, to their initial surprise, that it is constant. Then another bunch of people (largely one person) came up with a model - a bit of mathematics, otherwise known ...

1

There is only one real fundamental speed limit, $c$. Historically, we first discovered it in the context of light, so we call it the speed of light. In reality, it has a little bit deeper significance--it turns out all massless particles travel at $c$ and only at $c$, at least in vacuum. A massive particle can theoretically travel at any speed less than ...

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

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

To put it simply, it is Nature's way to preserve causality. From Wikipedia: "On the other hand, if signals could move faster than the speed of light, this would violate causality because it would allow a signal to be sent across spacelike intervals, which means that at least to some inertial observers the signal would travel backward in time. For this ...

1

Also, the fact that $\Delta t' \rightarrow 0$ if we formally let $v \rightarrow c$ can be interpreted as saying that no time at all passes for a particle moving at the speed of light. Photons cannot "age" or in any other way change over time.

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