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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 ...


4

One of ideas associated with string theory is the ekpyrotic universe. This starts with brane cosmology i.e. the idea that our universe is a four dimensional brane floating around in the ten dimensional string theory spacetime. There will be many such brane worlds and the ekpyrotic idea is that a collision between two branes would appear just like the Big ...


4

The reason for multiplying time by $c$ is to turn it into a distance i.e. it converts time to units of light seconds. In relativity there is an important invariant called the spacetime interval that is given by the metric. For example the flat space metric (the Minkowski metric) is: $$ ds^2 = -c^2dt^2 + dx^2 + dy^2 + dz^2 $$ The parameters $dx$, $dy$ and ...


4

The proper time of a time-like curve is its length.


3

I read a few lines about general relativity and [... an equation for] the eigentime of a time-like curve. I suppose that this is referring to an equation similar to $$\tau A_J^Q := \int_0^1~dt~\sqrt{g[~\dot\gamma, \dot\gamma~]},$$ where $A$ denotes a particular participant ("material point", "principal identifiable individual"), the quantity being ...


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


2

The relation $x_4=ict$ is a definition, and as such it doesn't prove anything. In particular, you cannot conclude that "the fourth dimension is moving" (whatever this means) based just on a definition. I could for example define $J_q=kt$, from which we would conclude that $\mathrm dJ_q/\mathrm dt=k$. Would you say this proves that $J_q$ is expanding? (note ...


2

If we think little more complex and consider every particle in the universe, each particle should be moving with some initial velocity caused by something happened before, due to some other particle You do not state the level of your physics knowledge. I will assume you are a highschool student. What you are describing is the way classical mechanics ...


1

Exactly as an ideal clock at rest with the observer (here pictured as a timelike curve) measures the proper time of the observer, ideal rulers at rest with the observer measure the distances in the rest space of the observer. Mathematically these rulers are pictured as an orthonormal basis made of $3$ vectors normal to the unit tangent vector to the ...


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According to the classic physics/Newton there was an absolute time in which things happens. But this intuitive persception of reality is left since Einstein proved that there is not an absolute time but a relative one depending on the observers'frame. Not our intuition is valid but what is measured. According to Newton, absolute time exists independently of ...


1

Nowadays it's reasonable to make an actual digital counter that operates at 10 GHz. Even so, you might rather use a prescaler to divide this frequency down to 1/4 or 1/8 of the microwave frequency before you actually start counting cycles. In olden times you might have generated your 10 GHz signal by multiplying up a lower frequency (maybe in the 100's of ...


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 ...



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