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How to pronounce beam of light in English?

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Welcome to relativity 104: special relativity in-depth. In relativity 104 we
will talk about the Lorentz transformation, which is the method used
to change reference frames according to the rules of special relativity.
Then we'll talk about how the Lorentz transformation leads to time dilation,
length contraction, and new rules for velocity addition, and then the
relativity of simultaneity. Next we'll talk about the Minkowski metric tensor
and the space-time invariant, which helps us measure distances in space-time.
Finally, we'll discuss relativistic dynamics, which explains how things like
forces, energy, and momentum behave in special relativity. And we'll also learn
about E = mc^2. This video will describe the geometry of the
Lorentz transformation visually and without equations. The actual Lorentz
transformation equations will come in the next video. So, back when we learned
Galilean relativity, we said that the laws of motion are the same in all
inertial reference frames. We also said that there is no special reference frame
that is stationary; all motion that we see is relative to something else.
When we plot motion on a spacetime diagram , we can see here that the scientist Einstein
is standing still and the car is moving off to the right.
But it's equally correct to say that the car is standing still and Einstein is
moving off to the left. Both diagrams are equivalent... they are just different points of view.
Another way to visualize changing reference frames in Galilean
relativity is to take a series of photographs as the objects move forward in time.
Here we can see that the world line of the car is diagonal and moving to the right.
And a beam of light is also traveling to the right, but much faster.
But the world line of the scientist is vertical. This means that we are in the
frame of reference of the scientist since he is standing still and his position is not changing.
If we want to change to the cars frame of reference according to the Galilean transformation,
we just shift the photographs over so that the cars world line is vertical.
We can see now that the scientist is moving off to the left.
And the beam of light is still traveling to the right, but at a slower speed.
We can also rearrange the time slices so that the beam of light has a vertical world line.
This means that the beam of light's position is constant and standing still.
We can even change the reference frame so that it is going faster than light.
And now the beam of light appears to be traveling left because it's not traveling fast enough
to keep up with the reference frame. And again this method of changing reference frames is
called the "Galilean transformation". Using the Galilean transformation we can see
that the speed of light is different in different reference frames. But this goes
against Einstein's second postulate of special relativity that the speed of
light in a vacuum is constant in all reference frames. To fix this, we need a
new transformation that leaves the speed of light unchanged when we go to a
different reference frame. This new transformation is called the "Lorentz transformation".
It was Lorenz who first discovered the transformation, not Einstein.
But Einstein was the first person to derive the transformation from the above two postulates.
Einstein derived this Lorentz transformation in his 1905 paper, which introduced special relativity.
The first thing that he did in this paper was to define the concept of "simultaneity".
"Simultaneity" is just a fancy way of saying when two events happen at the same time.
Einstein argued that when we assume the speed of light is constant for all inertial frames,
observers can no longer take for granted a universal definition of time for all
reference frames, as they do in Galilean relativity. So Einstein decided that he
needed to use light to define what it would mean for two events to happen at
the same time, because the speed of light is agreed upon by all inertial reference frames.
Before we start the derivation, I want to point out a small problem with space-time diagrams:
If we use everyday units on a spacetime diagram like "seconds" for time and "meters" for position...
A beam of light travels so fast at a speed of C = 300 million meters per second,
that it looks like a horizontal line. This makes it really hard to see what's happening.
For this reason, it's very common in special relativity to choose units of time and space
so that a beam of light travels one unit of distance in one unit of time.
For example, if time is in "seconds", then one unit of position is the
distance light travels in one second, which is 300 million meters, or one light-second.
You can see that the line for the equation of a beam of light x = c * t,
now travels one unit of distance for every one unit of time.
This means that a beam of light will always follow a diagonal line at 45 degrees to the horizontal.
With that out of the way, let's derive the Lorentz transformation,
which keeps the speed of light constant, using an example.
Let's say that Einstein is standing still on the ground, and physicists Marie Curie and Emmy Noether
are standing on either end of a moving train car. From Einstein's frame of
reference he is standing still and Marie and Emmy are moving towards the right.
But in the frame of the train, Marie and Emmy are standing still and Einstein is
moving towards the left. Now remember the first step in Einstein's paper was to
define "simultaneity": to define when things happen at the same time.
Let's say that Marie and Emmy would like to find a way to synchronize their clocks so that
they can decide when events happen at the same time. The two of them agree that
Marie will shoot a beam of light towards Emmy. When Emmy receives it, the beam of
light will be reflected back towards Marie. By symmetry, the time it takes for
the light beam to go from Marie to Emmy and the time it takes for the light to
go from Emmy back to Marie should both be equal to the same thing:
the distance between them "D" divided by the speed of light "C".
Marie and Emmy can now agree that this blue event point where the beam of light is reflected at Emmy's position
is simultaneous with this red event point which is halfway between the
time when Mary sends her light signal and receives it back again.
The fact that the light takes equal time to cross the train car in both directions is proof
that these two events in space-time are simultaneous and happen at the same time.
This shows us that in the train's frame of reference, events happen at the same time
will exist on the same horizontal line in the space-time diagram.
In other words the lines of simultaneity, which are the lines where events happen at the same
are horizontal lines in the train's reference frame.
This is true everywhere on the space-time diagram since we could
repeat the experiment with the reflected light beam at any time and place and get the same result.
Now let's look at this experiment from Einstein's point of view.
Einstein sees Marie and Emmy traveling to the right on their train car.
Now, remember that the speed of light is constant in all reference frames.
That means that beams of light will always travel at a 45 degree to the horizontal with a slope of 1.
So in Einstein's reference frame, since the train is traveling to the right,
when Marie sends her light beam to the right, it takes a little more time to reach Emmy,
since Emmy is basically running away from it. And since the second beam of light
is traveling to the left, it takes less time to reach Marie,
since Marie is basically running towards it. This is all according to Einstein's
frame of reference. Previously, in the frame of the train, Marie and Emmy found
their lines of simultaneity to be completely horizontal in the space-time diagram.
But in Einstein's reference frame, this is no longer true.
Remember that Marie and Emmy take this blue event point where the light beam is reflected
to be simultaneous with an event point halfway between when Marie
sends the first light beam and receives the second light beam.
If these two events are simultaneous for Marie and Emmy,
then their lines of simultaneity in Einstein's reference frame will be diagonal lines instead.
So if Einstein wanted to create a coordinate system for Marie's frame of reference,
he would tilt the time axis so that it is diagonal and aligned with her world line.
The time axis is located at a constant position in Mary's reference frame,
and so tilting it ensures we measure all positions relative to Mary.
We're already used to doing this in the Galilean transform. But the experiment we just did
suggests that we should also tilt the position axis. The position axis
should be aligned where all events happen at the same time. And since Marie's
line of simultaneity is tilted upward, her position axis should also be tilted upward.
This new tilted position axis will tell us how to measure time from Mary's point of view
So with the Galilean transform, when we change reference frames,
we just tilt the time axis so that it lines up with a moving
object's world line. But we keep the position access the same.
But now, in special relativity, we are proposing a new way to change reference frames:
the Lorentz transform. In the Lorentz transform, both the time and position axes get slanted.
The time axis is tilted to line up with the object's world line,
and the position axis is tilted to line up with a line of simultaneity in that object's reference frame.
So, the Lorentz transform involves changing the coordinate system
so that the time axis and the position axis sort of bend toward each other...
... kind of like the blades and a pair of scissors.
When the blades are spread apart, this is like when the time and position axes are at right angles.
But after the Lorentz transform, the axes close together, just like the blades on a pair of scissors close together.
So, we now have some intuition for what the Lorentz transformation looks like visually.
Now I'd like to prove that the speed of light is constant
when we change coordinates with the Lorentz transformation.
So, to start off I want to show you a simple geometric fact:
Imagine that we have a rectangle. If we draw this purple line between the opposite corners,
and then this other line between the other two opposite corners...
The point where these two lines cross should be the midpoint of both lines.
It should make sense, then, that these four line segments I've marked with blue tick marks
should all have the same length.
Now, if I cover up half of this rectangle, we get a right angle triangle.
So it's a theorem that if you take the midpoint on the longest side of a right angle triangle,
that this point is an equal distance from all three corners of the triangle.
The reason I bring this up is because if we look at the world line of the moving train in our space-time diagram,
and look at the beam of light that travels back and forth, we end up with a right angle triangle...
because beams of light always travel at 45-degree angles.
And remember, the midpoint of this world line we said was simultaneous
with the point where the beam of light is reflected.
And by the same logic as we used before, this midpoint is an equal distance
from all three corners of this right angle triangle.
Now, if we consider another line of simultaneity that's connected from
the origin, we can see that we get a parallelogram shape here. But it's not
just any parallelogram; it's a parallelogram where all four sides have
equal length. And this special parallelogram where all four sides have
equal length is called a "rhombus". And with a rhombus, the diagonal beam of
light that connects opposite corners will form equal angles with the time axis and the position axis.
So we've shown that a beam of light makes an equal angle
with the time axis and the position axis in the Lorentz transform.
When it comes to the Galilean transformation, the parallelograms we get
in the coordinate system are *not* rhombuses. One pair of parallel sides is
longer than the other pair. The result is that a beam of light traveling at a 45 degree angle
does not cut through the corners of the parallelogram.
This means that the beam of light does not travel one unit of distance in one unit of time.
And the result is that the speed of light can change depending on
the tilting angle we use for the Galilean transform.
But with the Lorentz transform, the coordinate system grid is made up of rhombuses,
and so the beam of light will always cut through the corners of the rhombuses diagonally.
This means that the speed of light always travels one unit of distance and one unit of time.
This fact is independent of the tilting angle for the time and position axes.
This shows us that the speed of light is the same in all reference frames
when we change reference frames using the Lorentz transformation.
So we've confirmed with the Lorentz transform that a beam of light
forms equal angles with the time and position axes.
So, to summarize this video, we invented a definition of simultaneity using beams of light.
We did this by sending a beam of light to the right and then reflecting it back to its source.
By symmetry, the event halfway between sending and receiving the light signal
should be simultaneous with the event where the beam of light was reflected.
When this is done in a stationary reference frame, the lines of simultaneity are horizontal.
When this experiment with reflected light beams is done on a moving reference frame,
the lines of simultaneity appear to be diagonal to an observer who is standing still.
We've shown that the Galilean transformation does not keep the speed of light constant in all reference frames.
This is because the Galilean transformation tilts the time axis to align
with the object's world line, but leaves the position axis the same.
And so a beam of light does not travel one unit of distance in one unit of time.
The Lorentz transformation does keep the speed of light constant in all reference frames.
because we tilt the time axis to align with the object's world line,
but we also tilt the position access to align with that object's lines of simultaneity.
The result is that the beam of light always travels one unit of distance in one unit of time.
We also proved that the time and position axes both make equal angles
with the beam of light that travels at 45 degrees in the space-time diagram.
In the next video we will derive the actual Lorentz transformation equations.

Welcome to relativity 104: special relativity in-depth. In relativity 104 we

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beam of light::noun | Spocien Dictionary

beam of light

noun

a column of light (as from a beacon)

Type	Words
Synonyms	beam, irradiation, light beam, ray, ray of light, shaft, shaft of light
Type of	light, visible light, visible radiation
Has types	low beam, moon-ray, heat ray, moonbeam, sunbeam, sunray, moon ray, high beam, laser beam

Examples of beam of light

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The lamp emits a focal plane beam of light as two white flashes every 20 seconds.

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Her silvery soprano seems like one more beam of light in Wilson's visual planning.

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So, while the beam of light is moving forward, the particles are moving backwards.

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A bright, narrow beam of light would shine through the holes of a Nipkow disk.

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The device allowed normal conversations to be transmitted on a beam of light.

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When Shane flicked the switch, a flame shot out rather than a beam of light.

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There are some elements of staying out of a cone of detection, like a beam of light.

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How to pronounce beam of light in English?

beam of light::noun | Spocien Dictionary

abandonment

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