# Proofing a few paragraphs on relativity

#### jason_one

I have to write a brief history of physics for this english paper I'm doing. The only part I don't have a strong knowledge of is relativity, so if anyone would like to check the following three paragraphs for me and tell me if I summed it up accurately, I would be very grateful.

"Einstein stated that the speed of light will remain constant for all observers no matter what their velocities are. This means that if I, at rest, observe a beam of light, I will see it traveling at 186,000 miles per second. Now, say I witness a man flying past me at a constant rate close to that of the speed of light. This does not mean that he will observe light traveling very slowly, but rather his sense of time has slowed down so that, to him, light still appears to travel at 186,000 miles per second. In fact if he had a watch on, I would see his watch as moving more slowly than mine. But, because in his frame of reference he is the one at rest and I am the one moving at close to light speed, he will observe that my watch is moving more slowly compared to his. This is called 'time dilation'. And not only will his clock appear to be slowed down to me, but he will also appear smaller to me and vice versa. If the two of us held out meter sticks, his would appear smaller than mine to me, and mine would appear smaller than his to him.

It is because of this nature of spatial and temporal relativity, Einstein concluded that the three dimensions of space and the single dimension of time are not absolute and independent of each other, but they make up a four-dimensional space-time continuum which is relative to the observer.

Einstein stated, in his General Theory of Relativity, that gravity is not a force that exists in space, as Newton had thought, but is actually a curvature of space-time itself. Einstein understood that being in a gravitational field was the equivalent to being in state of acceleration, which brought about a warp, or curve, in the fabric of space-time. This means, therefore, that time and space flow differently in different parts of the universe according to the distribution of mass."

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#### Berislav

but they make up a four-dimensional space-time continuum which is relative to the observer.
Might I suggest better wording for this sentance. Four-vectors are Lorentz invariant, someone might think otherwise after reading that.

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#### JesseM

Science Advisor
jason_one said:
This does not mean that he will observe light traveling very slowly, but rather his sense of time has slowed down so that, to him, light still appears to travel at 186,000 miles per second.
Time dilation is part of the explanation for why he still sees the light travel at 186,000 miles per second, but it isn't the only part. If his rulers didn't contract relative to yours, or if his definition of simultaneity wasn't different than yours, then he wouldn't measure the same light beam to be moving at 186,000 miles per second even if his clocks did slow down.

#### learningphysics

Homework Helper
Berislav said:
Might I suggest better wording for this sentance. Four-vectors are Lorentz invariant, someone might think otherwise after reading that.
The four-vectors are not themselves Lorentz invariant. Their magnitudes are lorentz invariant.

#### Berislav

The four-vectors are not themselves Lorentz invariant. Their magnitudes are lorentz invariant.
I didn't want to seem pedantic with my previous post but yes, you are right, the Minkowski norms of four-vectors are Lorentz invariant, not the vectors themselves.

#### jason_one

Thanks for the help guys!

#### EnumaElish

Science Advisor
Homework Helper
And not only will his clock appear to be slowed down to me, but he will also appear smaller to me and vice versa. If the two of us held out meter sticks, his would appear smaller than mine to me, and mine would appear smaller than his to him.
To you, he would appear compressed in the direction of his movement, to be precise (or picky, one might say). Similarly his meter would appear shorter to you assuming both you and he are holding the respective meters parallel to each other's vector (arrow) of motion. If the meters are held vertically (perpendicular to motion's arrow), then they will appear only thinner relative to each other.

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