special relativity: physics at the speed of light
Yes, you are traveling international.
Star freighter Hyperion, I\'m out of Hong Kong.
Substances from the vortex of the Milky Way
The automation system has just brought you back from the suspended animation.
Ship maintenance is carried out regularly.
Climbing out of your sleeping room, you turn on the system status.
All systems are nominal, no problem. That is good.
30 kilometers for your captain.
Just carry out daily maintenance and exhaustion of body and mind;
You don\'t need extra work.
You are considering the task of the freighter.
Hyperion and its three sister ships crossed the flight to harvest energy in reverse formmatter.
Collect millions of watts per trip
Hours, enough to support 35 billion human and perceptive robots in the solar system for a whole year.
Look up at the scanner screen and you will see the middle
About a light flying space stationhour ahead.
The space station has 4 floats, which are arranged in a square with 30 kilometers on one side.
A series of 11 stations keep your boat running for two years from Earth.
You check the speed of the freighter relative to the float
It\'s about 50% of the speed of light, but the same thing is, I. e.
No acceleration or deceleration.
This makes sense. at mid-
The freighter has entered a transitional phase of acceleration and deceleration.
Through thoughtful research, or media coverage, you may have heard of relativity, Einstein\'s masterpiece.
Einstein established his theory in two stages.
First, special relativity, covering non-
Acceleration frame of reference, second, general relativity, involving acceleration and gravity-
Reference framework for binding.
Special relativity gives the famous E = MC squared equation, covering the physical properties of objects close to the speed of light.
General relativity helps reveal the possibility of a black hole and provides the physical properties of an object in a gravitational field or accelerating.
Here we will explore the special theory of relativity using our hypothetical ship Hyperion.
The speed of this freighter is a large part of the speed of light, which determines our use of special relativity.
The calculation based on the Law of daily speed movement, such as the law of motion of aircraft and cars, will produce incorrect results.
It is important, however, that our cargo ship has neither accelerated nor slowed down, and has gone deep enough into space, and gravity has weakened to a negligible level.
Therefore, the consideration of general relativity has not entered here.
In vacuum special relativity, waves and light begin with basic, basic statements, and all observers, regardless of their motion, measure the same speed of light.
Whether it is a hundred kilometers per hour, or a million kilometers per hour, or a billion kilometers per hour, all observers measure the speed of light to 1.
8 billion kilometers per hour
It should be noted that the observer is not accelerating or under the strong gravitational field.
Nevertheless, why is this happening?
Why does the speed of the observer not affect the speed of light measured?
If two people throw baseball, one on a moving bullet train and the other on the ground, the bullet train\'s games increase the speed of throwing the ball.
So, shouldn\'t the speed of light be increased by the speed of space craft?
That\'s what you think.
But unlike baseball, the speed of light remains the same regardless of the speed of the observer. Why?
Let\'s think about the waves.
Most waves, whether they are waves in sound waves, waves, waves in violin playing strings, or shock waves through solid Earth, are made up of motion through the medium.
Sound waves are composed of moving air molecules, sound waves are composed of moving water packets, sound waves are composed of the movement of strings, and shock waves are composed of vibrations in rocks and soil.
In contrast, in sharp contrast, the fluctuation of light does not include the movement of any underlying substrate.
The propagation of light does not require any supporting medium.
The key difference is this.
Let our work think that in the international context
Star cargo ship.
You rise from the suspended animation
The acceleration stopped.
In this case, there is no buoy nearbyby.
How do you know you\'re moving?
How do you define movement?
Because you live deep in space, far away from the buoy, there is no object nearby
Measure your speed by this.
The vacuum does not provide a reference point.
Einstein and others thought of it.
They have Maxwell\'s laws of electrodynamics, and the velocity of light in vacuum is given from the first principle.
Now, if there is no reference point in a vacuum measuring the speed of a physical object, any reference point can (non-accelerated)
The motion is a motion of privilege?
Will there be a special motion (aka speed)
The Observer obtains the speed of light of \"real\", while other observers move at different speeds and are affected by the speed of light of the observer\'s motion.
Einstein, in particular, came to no conclusion by physicists.
If there is a privileged reference framework
Privileged speed will find that light violates Maxwell\'s law.
Maxwell\'s law is very reasonable. Instead of modifying these laws, physicists have proposed a new hypothesis --
Relative speed does not change the speed of light. Ahh, you say.
You can see the way to determine if Hyperion is moving.
Just compare its speed to the buoy;
They\'re fixed, right? Really?
Will they not move relative to the center of our galaxy?
Isn\'t Our Galaxy moving relative to other galaxies?
So who or what can\'t be moved here?
In fact, if we consider the whole universe, we cannot judge the \"real\" speed that the object has, only relative to the speed of other objects.
If there is no reference point to provide a fixed frame, if we can only determine the relative velocity, Maxwell\'s law, and the nature of the universe, all observers are instructed to measure light at the same speed.
The contraction of time if the speed of light remains the same, what will happen?
It must be different.
If I move at a speed close to the speed of light relative to you (
Remember, we can tell each other the speed;
We can\'t tell some generally fixed reference absolute speed)
We measure the same light pulse, and one of the uses seems to be to catch up with the light pulse.
So there must be some distortion in the measurement.
Let\'s go back to our cargo ship.
Imagine Hyperion moving from right to left relative to the buoy.
As mentioned earlier, the buoy forms a square at 30 kilometers per side (
According to the static measurement relative to the buoy).
When Hyperion enters the buoy configuration, its front end cuts an imaginary line between the right two floats.
It enters at right angles to this imaginary line, but is significantly off center, only a few hundred metres from one right buoy and nearly 30 kilometres from the other right buoy.
Like the front of the freighter cutting off the line, the near right buoy emits a light pulse at the front of the freighter to the second right buoy 30 kilometers away.
The light went out, hit the second right buoy, and then bounced back to the first right buoy, 60 kilometers round-trip.
Light travels at a speed of 300,000 kilometers per second, rounded or 0.
3 kilometers in a microsecond (
One minute per million)
200 micro round-trip consumption of optical pulseseconds.
The result is to divide the round trip of 60 kilometers by 0.
3 kilometers per Microsecond.
This calculation is valid for observers fixed on the buoy.
It doesn\'t work for you on Hyperion. Why?
Hyperion moves when the light travels to the second right float and returns.
In fact, the speed of Hyperion relative to the buoy is like this, and when the light pulse returns, the rear of the freighter reaches the first right buoy.
From our vantage point, how far did the light travel on the cargo ship?
First, we realize that the light travels along the triangle from the front of the ship to the second right buoy and then back to the back of the ship.
How big is the triangle?
The right-most buoy is 30 kilometers from the first right buoy, so the triangle is 30 kilometers high. e.
The second buoy on the right.
The bottom of the triangle extends 30 kilometers.
The length of the ship.
Once again, let\'s imagine the journey of light.
In the reference frame of Hyperion, the light passes through the front of the ship, hits the second right buoy, and then returns to the back of the freighter. Some geometry (
The triangle showing 30 high 30 at the bottom will measure 33.
Along each sloping edge.
We get this by dividing the triangle into the middle, 15 by 30 to two right-angled triangles.
Then add 15 and 30 and get 1125, where the square root gives 33. 5.
So, in our frame of reference, the light travels 67 kilometers. e.
Along both sides of the triangle. At 0.
3 kilometers per Micro
Second, we measure the pulse of light at just over 223 micro. seconds.
Remember, the Observer we fixed on the buoy measured the time travel at 200 macro. seconds.
This reveals the first turning point of measurement.
In order to keep the speed of light unchanged for all observers, clocks moving relative to each other will measure the same event at different times.
In particular, for us, on Hyperion, the clock on the buoy is moving, and the time for the clock measurement is shorter.
Therefore, the clock moves slowly relative to the stationary clock.
Again, this is a turning point.
The clock moving relative to the observer is slower than the clock that is still relative to that observer. But wait.
What about the observer on the buoy?
Didn\'t they say they were still?
They will come to the conclusion that the still clock is a little slower.
We have a subtle difference.
Compared to us, we can synchronize the still clock.
So we can use two clocks, one at the back of Hyperion and the other at the front to measure 223 micro.
The second propagation time of the beam.
We cannot move the clock synchronously or assume it.
Therefore, in order to compare the propagation time of light in moving reference frames and still reference frames, we must measure events in moving reference frames with the same clock.
For observers on the buoy, Hyperion is moving, and on Hyperion, events are measured on two different clocks.
With this in mind, observers on the buoy cannot use our two measurements to figure out which clock is going slowly.
The de-coupling of the clock\'s de-coupling of the clock speed, a phenomenon that runs slower relative to the clock we move, produces a second twist: The clock that moves relative to US becomes from our time
Let\'s finish this.
Hyperion completed the shipment and the ship will have an engine upgrade once it returns to the solar system.
Two levels now.
The third speed of light in the middleflight.
This higher speed further expands the difference in measurement time.
In the example above, at about half the speed of light, the moving frame of reference measures an event at 89% of what we measure (200 over 223). At two-
Third, the speed of light, this deceleration, this time expansion, expand to 75%.
Activities lasting 200 micro
Seconds measured on the mobile clock will measure 267 Micro
On the freighter, there are a few seconds on the clock next to us. We reach mid-flight.
When we passed the right buoy, we read its clock.
For ease of comparison, instead of handling hours, minutes, and seconds, we only handle the position of the hand on the micro-computersecond clock.
When the front of Hyperion passes through the buoy, the buoy clock reads 56 micro
A few seconds before zero.
We read 75 micro
A few seconds before zero.
So the float clock reads slightly faster than ours.
Remember, we think we are moving forward.
However, from our point of view, the buoy clock moves relative to us, while the clock on our cargo ship is still relative to us.
Therefore, the float clock is a clock that moves the clock and therefore runs at a slower speed.
With Hyperion reaching 2 out of 3 with respect to the speed of light of the buoy, the buoy passes by us at a speed of 0.
2 kilometers per Microsecond (
The speed of light is 0.
3 kilometers per Microsecond).
So through our clock, the buoy moves from the front of the freighter to the midpoint at a distance of 75seconds (
Divide 15 kilometers by 0.
2 kilometers per Microsecond).
Cargo wheel clock sync (
A complicated procedure but feasible)
So we see the Micro
Zero micro seconds-
In seconds of our clock.
What did we see on the buoy?
We know its clock is running slower.
How much slower?
The square root of the \"public test\" factor (
1 reduction in speed Square).
This beta factor comes exactly from the mathematics of bidagolas above, but the details of this article do not matter.
Simply remember the key attributes, I. e.
The moving clock runs slower and the equation-
A tie (relatively)
A simple stock-hook theorem
There is how slow the calculation is.
The beta factor of 2 out of 3 light is equivalent to about 75%.
So if our clock is advanced 75 micro
The time from the front to the middle is a few seconds.
Section, float clock advanced 75% M 75 or 56 microseconds.
Float clock read 56 micro
When the clock passes through the front of Hyperion, it is a few seconds earlier than zero, so it now reads zero.
Now the float can go further through the back of the Sea Wave Dragon.
15 kilometers more.
Our clock is up to 75.
Seconds, while the float clock only rises to 56seconds.
This progress reveals a key phenomenon.
The moving clocks are not only slow, but the time for those clocks to read is also different.
At some times, those moving clocks read earlier than the still ones, and sometimes they read later than the still ones.
Therefore, we will see moving objects in our past or future thinking. Very spooky.
So, what kind of vision do we have for the future?
Can we somehow gather information about the mobile reference framework and tell them what will happen?
Or did they inspire us? No.
We may see the buoy at some point in the future (
When the buoy passes through the front of Hyperion, its clock is displayed as 56 micro-
A few seconds before zero, or19 Micro
A few seconds earlier than our clock).
However, we have not yet seen the buoy at the same time. e. 75 micro-
A few seconds before zero.
In order to deceive the time, in order to tell the buoy its future, we need to get the information from one point in time and convey it to another point in time.
But this will never happen.
We see the buoy in the future, in the present, in the past, but in this case, we do not see the buoy at another point in time.
Therefore, we cannot convey any future knowledge to the buoy.
Let\'s summarize it quickly.
The law of nature requires all observers, regardless of movement, to measure light at the same speed.
This means and requires that the clock tick speed relative to the observer\'s movement will be slower, and further implies and requires that the time registered on the mobile clock start with the time registered on the clock fixed on us.
Do we have more meaning? Yes.
The constant nature of the speed of light requires and specifies that the length of the moving object is consistent.
When the buoy accelerates at a specific moment, Hyperion should be aligned with the buoy.
Our 30-kilometer length is equivalent to a 30-kilometer buoy interval.
So when our ships align themselvesby-
On one side of the buoy, the Observer before and after Hyperion should see the buoy.
But this did not happen.
Our watchers on Hyperion don\'t see the buoy in the middle.
Hyperion\'s Ship Point is aligned with the midpoint between the buoy.
In fact, in this arrangement, the Hyperion observer must turn his gaze to mid-
The boat went to see the buoy.
At the alignment of mid
The midpoint between Hyperion\'s boat and the buoy, each of which is more than 3 kilometers from the end of Hyperion. What happened?
Why don\'t we measure buoy 30 kilometers apart?
What caused the distance of 30 kilometers to be reduced by nearly 7 kilometers?
What happened, what we encountered, representing another branch of the speed of light\'s permanence, specifically, we measured the time of moving objects shorter than the time of measuring stationary objects.
How does this happen?
Let\'s reveal this by assuming that we measure a moving buoy 30 kilometers apart and then do some math with this assumption.
We will find that we will encounter contradictions.
This suggests that our assumptions are incorrect.
Let\'s run the calculations.
As mentioned above, we will assume that we measure the buoy 30 kilometres apart.
Under this assumption, the buoy will be aligned with the end of Hyperion.
For our experiments, at the moment of alignment, we emit the beam from the end of Hyperion to the middle.
In order to keep the line straight, we need to mark the distance on Hyperion and the buoy.
We will label both ends of Hyperion plus 15 kilometres (the right end)
15 kilometres less (the left end)
, Extension, the middle of the ship will be zero.
Hyperion clock will read zero micro
A few seconds at the beginning of the beam.
We will also mark the buoy as negative 15 km and negative 15 km and extend to the point of equal distance between the buoy with a distance of zero.
A clock will be placed at the zero point of the buoy.
That clock will read zero.
A few seconds in the middle
The ship on Hyperion is aligned with the midpoint of the buoy.
Now let\'s follow the beam.
Of course, they will compete with each other before they meet.
On Hyperion, this convergence occurs in the middle of the distance mark zero.
Each beam travels for 15 kilometers.
The given light is at 0.
3 kilometers per Micro
Second, the beam is 50 microseconds.
The buoy passes by Hyperion at a speed of 2 or 0 out of 3.
2 kilometers per Microsecond.
In 50 micro
After a few seconds of light gathering, the buoy will move. How much?
We multiply their speed by 0.
2 kilometers per Micro
The second 50 micro
Seconds, 10 kilometers.
In this 10-kilometer movement, when the beam gathers, our zero points are aligned with their negative 10-kilometer points.
Keep in mind that if the trip to Hyperion is correctto-
Left, then on Hyperion, we look at the buoy when driving on the left-to-right.
On Hyperion, we see the same propagation distance for each beam.
What about the observer in the mobile framework? e.
Moving with a buoy?
They saw the beam at different distances.
The beam starts on the right, plus 15, and travels one way to minus 10 kilometers in the buoy reference frame.
Represents a travel distance of 25 kilometers.
Light from the left, minus 15 degrees, only 5 kilometers. e.
From minus 15 kilometers to minus 10 kilometers.
Of course, these unequal travel distances will occur because the buoy will move during the beam travel.
In the frame of reference of the buoy, one beam travels 20 kilometers further than the other.
In order for them to meet at the same time, when another beam covers an additional 20 kilometres, the beam with a shorter travel distance must wait.
How long have you waited? At the 0.
3 kilometers per Micro
The second is 66. 7 micro-seconds.
Let\'s think about it.
In our fixed reference frame, each beam starts from time and is equal to zero on the clock at both ends of Hyperion.
However, for the buoy, the light will leave a buoy, the distance of the buoy plus 15, 66. 7 micro-
A few seconds earlier than the distance minus 15 seconds to leave the buoy.
At the beginning of this experiment, we set the clock in the middle.
The point between a buoy whose time phase is equal to zero.
By symmetry, use this 66. 7 micro-
The second difference is that the clock with a negative 15 point must be read plus 33. 3 micro-
Seconds, plus the 15-point clock must read minus 33.
3, when the beam leaves.
What about the intersection of minus 10 in the buoy reference frame?
When the beam leaves, when is the intersection point in the buoy reference frame?
Keep in mind that the intersection point in the frame of reference of the buoy is negative 10 kilometers.
If the minus 15 is 33. 3 micro-
Seconds, minus 10: 22. 2 micro-seconds.
We now pull the clock in and run slower in the moving frame.
At the speed of light of 2 out of 3, the clock runs at 75% (
Or rather 74. 5%)
We fix the clock rate in the frame.
Given that our clocks measure 50 micrometers
For the propagation time of the light, the clock on the buoy measures the propagation time of the light for 37 seconds. 3 micro-seconds.
In addition, we also got the meeting time in the buoy reference frame.
The clock reading at the meeting point is 22. 2 micro-
When the light is turned on, 37 in advance. 3 micro-
Travel in light for a few seconds.
Therefore, our meeting time is 59 years old. 5 micro-
Move the second in the reference frame, I. e.
Buoy reference frame.
Now the contradiction is coming.
Light starts at 33 minus 15. 3 micro-
Seconds and reach minus 10 at 59. 5 micro-seconds.
Then call it a 26 micro.
Time for the second trip
The travel distance is 5 kilometers.
Implied speed, me. e.
5 kilometers divided by 26 micro
The second trip time, come out 0.
19 kilometers per Microsecond.
From the other end, the light traveled 25 kilometers in 92. 8 micro-seconds (from minus 33. 3 to plus 59. 5).
Implied speed, me. e.
25 kilometers divided by 93 Micro
The second trip time, come out 0.
27 kilometers per Microsecond. No good.
Light in 0.
3 kilometers per Microsecond.
When we assume that we will measure the buoy 30 kilometres apart and adjust the clock to accommodate this assumption, we do not get the speed of light.
Keep in mind strictly that all observers must measure the speed of light at the same speed.
To achieve this, the clock speed, the relative time reading, and even the distance must be adjusted.
To align the buoy with the end of Hyperion, how far does the buoy need to be apart?
They need to be 40 years old.
2 kilometers apart
40 with buoy.
2 kilometers apart, when in the middle, the front and back of Hyperion will be aligned with the buoyship (Hyperion)
Middle point (of the buoys)align.
Amazing, almost impossible to understand.
All observers need to measure the same speed of light, which requires us to measure the speed of moving objects much shorter than at rest.
If we adopt these 40, what will the float clock read.
2 kilometers apart?
When the boat is aligned with the buoy, the left buoy clock will read plus 44. 7 micro-
Second, the right float clock reads negative 44. 7 micro-seconds.
Because the beam is emitted when the vessel is aligned with the buoy, the beam on the right leaves 89. 4 micro-
A few seconds before the beam on the left, in the buoy frame of reference.
This time difference is equal to the right beam 26.
8 kilometers before the start of the left beam, as shown in the buoy frame of reference.
Then both beams move 6.
Until they met seven kilometers. The 26. 8 plus 6.
The total number of two times reached 40.
2 kilometers between the buoy.
The left beam starts at a position minus 20.
1. Time plus 44. 7 micro-
Seconds, trip 6. 7 kilometers. Light needs 22. 4 micro-seconds (6. 7 divided by 0. 3)
Travel 6. 7 kilometers.
Therefore, the clock of negative 13. 4 point (minus 20.
2 kilometers plus 6.
The left beam travels 7 kilometers)should read 67. 1 micro-
A few seconds when the left beam gets there. Does it?
Proportionally, a clock with a negative 13 when the buoy and Hyperion are aligned.
Read at 4 plus 44. 7 minus one-sixth of 89. 4. One-sixth of 89. 4 is 14. 9, and 44. 7 minus 14. 9 would be 29. 8 micro-seconds.
Now keep in mind that the float clock must be 37 in advance. 3 micro-
A few seconds during the beam propagation.
This is because on Hyperion, it takes 50 micro for beam travel
The buoy clock must be 75% times slower in seconds (
Or rather 74. 5 percent). Add the 29. 8 and the 37.
We got 67 points. 1 micro-seconds.
We said earlier that the clock of minus 13.
67 should be read 4 kilometers. 1 micro-
Seconds when the left beam arrives. And it does.
Separate the buoy 40.
Therefore, 2 kilometers align the clock and distance on the buoy so that they measure the correct speed of light.
Will moving objects really shrink?
Does the atomic distortion of an object cause the object to be shorter? Absolutely not.
Think about what we read on the clock.
When the clocks on Hyperion all read the same time, the clocks in the moving reference frame are all ready for a different time.
The moving distance is reduced because we can see different parts of the moving object at different times.
40 with buoy.
2 kilometers apart (
Measure at rest)
We saw the left buoy on the plus 44. 7 micro-seconds (
In its reference frame)
Right buoy at minus 44. 7 micro-seconds.
Let\'s take a look at another way to envision a length contraction, in a more downward caseto-Earth example.
Imagine a freight train with a length of 4 kilometers, traveling at a speed of 40 kilometers per hour.
You and an experimenter stand on the rails three kilometers apart.
When the front of the train passes you, you will signal your partner.
Your partner waited 89 seconds to write down the part where the train is now passing in front of him.
What did he see?
The end of the train.
The four-kilometer train is within a three-mile distance between you and your experimenter companion.
This is because your partner is watching the train later than you.
The speed at which the moving object affects the measurement is not accurate.
In our train example, we created two different viewing times by waiting.
In the case of Hyperion, we don\'t have to wait-
The near-light passing speed of the buoy makes a difference in the clock observation time.
While not an exact analogy, the simplified train example does motivate the measurement of the length of an object at two different times to distort the measurement.
The example of the train also shows that we can shorten the measurement length of the object without physical shrinkage.
While shrinkage does not really happen, the difference in timestamp is true.
In our Hyperion example, using beams, if we go back and pick up the clocks on the buoy, those clocks record that the beams we send do start from 89. 4 micro-seconds apart.
We\'ll look at our Hyperion clock, and our Hyperion clock will really show up in our reference frame where the beam starts at the same time.
Is the clock smart?
How does the clock \"know\" how to adjust itself?
Do they feel the relative speed and use some kind of intelligence to readjust themselves?
Despite any other appearance of the clock, it does not feel any movement or make any adjustments.
If you stand next to the clock and the object passes by you at a speed close to the speed of light, nothing happens to the clock next to you.
It does not make any adjustments, changes, or compensation in order to pass the object.
Instead, the geometry of space and time will allow the observer to see the moving clock ticking more slowly and the moving object is measured less.
If you leave me, I measure you with a ruler in my hand, and the height you measure will shrink in proportion to the distance you are from me.
When you leave, the result that you look smaller is that the angle between the light of the head and the light of the foot is smaller.
The light does not need to know what to do, and the ruler is not adjusted.
Instead, the geometry of our world determines that you measure less when you leave.
Again, if I put the lens between you and the screen, I can expand or narrow your height by adjusting the lens.
Light does not need to know how to adjust;
Light just follows the laws of physics.
I can measure your height with distance and lens.
I can easily write formulas for these measurement changes.
Again, the moving clock reads more slowly in terms of the nature of time.
We think the clock needs to \"know\" how to adjust, as our general experience at low speeds suggests that the clock runs at the same speed.
But if we were born on Hyperion and live at a speed close to the speed of light, the slowing down of the clock is as familiar to us as the bending of the beam as it passes through the lens due to relative motion.
All observers must measure the same speed of light.
The properties of nature, the geometric facts of space and time, create the inverse
The observation of time and space is intuitive, but it is a real adjustment.
Moving clocks run more slowly, they become uncoupled from our time, and the length of any object moving with these clocks is shorter.