B Lightwatch/Lightclock (Lichtuhr)

[A.T.]

You have a horizontal surface emitting a wave front simultaneously in the frame of the emitting surface. The resulting wave front propagates vertically in the frame of the emitting surface.

From the viewpoint of a rest frame compared to which the surface is moving, the emission is not simultaneous. Instead, the emission event sweeps across the moving surface and the emitted wave front emerges at an angle and propagates at an angle.

Of course it is the same wave front viewed from two different perspectives.

Here is a paper that has some images visualizing this:
https://arxiv.org/pdf/physics/0409013.pdf

 

[vanhees71]

Some translations of German language relativity books used the English word "velocity" for the German word for "speed".

The problem is that in German we don't have enough words to be as precise as in English. The most severe example that in German we have only "Wissenschaft", in English you have the very important difference between science ("Naturwissenschaft") and humanities ("Geisteswissenschaft"), which are two distinct incompatible worlds...

 

[A.T.]

The problem is that in German we don't have enough words to be as precise as in English. The most severe example that in German we have only "Wissenschaft", in English you have the very important difference between science ("Naturwissenschaft") and humanities ("Geisteswissenschaft"), which are two distinct incompatible worlds...

Seems like it's not a matter of "not enough words", but how words are formed: invent completely new ones vs. combine existing ones.

 

[Ibix]

Seems like it's not a matter of "not enough words", but how words are formed: invent completely new ones vs. combine existing ones.

Actually, English being a bit of a mix of both germanic and latin derived languages, we often have two words for more or less the same thing. We just seem to have repurposed the germanic-rooted and latin-rooted words for "how fast is something going" to mean different things in scientific language.

 

[A.T.]

Actually, English being a bit of a mix of both germanic and latin derived languages, we often have two words for more or less the same thing.

Yeah, "invent" wasn't the right term here.

 

[vanhees71]

Seems like it's not a matter of "not enough words", but how words are formed: invent completely new ones vs. combine existing ones.

Well, in German you simply say "Geschwindigkeit (velocity)" for both the vector (velocity in English) and its magnitude (speed in English).

 

[PeroK]

Well, in German you simply say "Geschwindigkeit (velocity)" for both the vector (velocity in English) and its magnitude (speed in English).

Why not "Geschwindigkeitsgröße" for speed?

 

[Ibix]

Well, in German you simply say "Geschwindigkeit (velocity)" for both the vector (velocity in English) and its magnitude (speed in English).

Presumably you can construct "velocity vector" and "velocity magnitude" when necessary. I guess the problem is that as an author you might rely on context to convey to other physicists that you mean the magnitude when you write "Geschwindigkeit". But a naive translation into English as "velocity" causes trouble for English readers.

 

[A.T.]

Well, in German you simply say "Geschwindigkeit (velocity)" for both the vector (velocity in English) and its magnitude (speed in English).

Your example is rather an exception. There is no special English word for "magnitude of force" or "magnitude of acceleration".

In German you simply attach "...betrag", to explicitly refer to the magnitude: "Geschwindigkeitsbetrag", "Kraftbetrag" (etc.).

I don't think using a completely different word for the magnitude of a vector is helpful. And it's not more precise than "magnitude of ... / ...betrag", just shorter. But you have to learn more unique words.

 

[vanhees71]

Why not "Geschwindigkeitsgröße" for speed?

Hm, that would a good solution, but I've not seen it used anywhere. If you want to emphasize it's the magnitude you say something like "der Betrag der Geschwindigkeit". That's why German texts are usually longer than their English translation ;-).

 

[vanhees71]

Presumably you can construct "velocity vector" and "velocity magnitude" when necessary. I guess the problem is that as an author you might rely on context to convey to other physicists that you mean the magnitude when you write "Geschwindigkeit". But a naive translation into English as "velocity" causes trouble for English readers.

Sure, and I apologize for being part of the wide abuse of the English language as the lingua franca of science, which is rather "broken English"...

 

[vanhees71]

Your example is rather an exception. There is no special English word for "magnitude of force" or "magnitude of acceleration".

In German you simply attach "...betrag", to explicitly refer to the magnitude: "Geschwindigkeitsbetrag", "Kraftbetrag" (etc.).

I don't think using a completely different word for the magnitude of a vector is helpful. And it's not more precise than "magnitude of ... / ...betrag", just shorter. But you have to learn more unique words.

Well, another problem with mechanics at the university level is that you first have to get out the sloppy introduction to the subject in high schools. One of the didactical sins is not to hammer into students' heads that velocity is a vector, a vector and only a vector (the same holds of course true for force, torque, momentum, angular momentum). It's in a way understandable since of course you want to teach some physics also to young students (because otherwise they won't get interested in the STEM subjects at all), and there a full vector treatment is way too complicated. It's a dilemma!

 

[Martin68]

I apologize for all that mess, that was not my intention

In German we have:
Geschwindigkeit - can be both, vector and amount
Geschwindigkeitsvector - the vector
Geschwindigkeitsbetrag - the amount

What would be the correct translation for that three things?

 

[vanhees71]

It's correct "Geschwindigkeit" can mean both, vector and magnitude. You must infer it from the context. "Geschwindigkeitsvektor" is "velocity" and Geschwindigkeitsbetrag is "speed". Maybe, I'm wrong and native speakers have to correct me!

 

[Martin68]

vektor

... I'm a programmer and for me it's early in the morning

 

[PeroK]

I apologize for all that mess, that was not my intention

In German we have:
Geschwindigkeit - can be both, vector and amount
Geschwindigkeitsvector - the vector
Geschwindigkeitsbetrag - the amount

What would be the correct translation for that three things?

Speed, velocity and magnitude of velocity.

In general in physics a vector is a quantity whose components transform between reference frames according to certain rules. And a scalar is a quantity that is invariant in different reference frames.

The light postulare of SR effectively says that the speed of light is a scalar. Whereas, the speed of a particle with mass is not a scalar.

 

[vanhees71]

To be pedantic: Vectors and tensors are not dependent on any choice of a basis. Of course the vector and tensor components depend on the basis they refer to. Physicists are very sloppy in saying "a vector or tensor is an object that transforms in this or that way". Correct is "vector or tensor components transforms in this or that way".

 

[Martin68]

tensors

This word I never heard before (but looked now in wikipedia)

 

[jtbell]

I don't think using a completely different word for the magnitude of a vector is helpful. And it's not more precise than "magnitude of ... / ...betrag", just shorter. But you have to learn more unique words.

Off the top of my head, velocity is the only vector quantity for which English-speaking physicists and textbooks (American ones at least) use a separate word for the magnitude (speed).

I have a vague memory of reading somewhere that the speed vs. velocity distinction originated in the early 1900s, probably in a then-new textbook which became widely used. It's been universal at least since I started studying physics seriously c. 1970.

Ah, I just remembered another such pair: [vector] displacement vs. [scalar] distance, whose time-derivatives give velocity and speed.

 

[Ibix]

I have a vague memory of reading somewhere that the speed vs. velocity distinction originated in the early 1900s, probably in a then-new textbook which became widely used.

It's a funny one, isn't it. In some ways it would be easier to use the words speed and velocity interchangably and append "vector" or "magnitude". That's closer to the non-technical English usage, and people seem to have no trouble with the distinction between "my speed was 30mph" and "my speed was 30mph northbound" when direction matters or not.

 

[weirdoguy]

velocity is the only vector quantity for which English-speaking physicists and textbooks (American ones at least) use a separate word for the magnitude (speed)

Same in polish. But some authors try to avoid it. It really gets messy in basic schooling in the context of mean velocity and mean spead, where we have 'magnitude of mean velocity' and 'mean magnitude of velocity'. It's hard for children to grasp the difference. I prefer to use word speed, it makes life easier.

 

[vanhees71]

Ah, I just remembered another such pair: [vector] displacement vs. [scalar] distance, whose time-derivatives give velocity and speed.

That seems not to be true since on the one hand speed is
$$|\vec{v}|=|\dot{\vec{x}}|,$$
i.e., indeed the magnitude of the velocity, but
[edit: corrected typo in view of #56]
$$\dot{r} = \mathrm{d}_t |\vec{r}|=\mathrm{d}_t \sqrt{\vec{r}^2}=\vec{r} \cdot \dot{\vec{r}}/r,$$
which in general is not $|\vec{v}|$.

 

[Martin68]

dt√˙→r2=→r⋅˙→r/r

Not necessarily I have to understand it ... ... but, why is the derivation of r squared and drawn root the same as the amount of r? And the next step I do not understand at all
(But, no problem)

 

[DrGreg]

Not necessarily I have to understand it ... ... but, why is the derivation of r squared and drawn root the same as the amount of r? And the next step I do not understand at all
(But, no problem)

$$
r = |\mathbf{r}| = \left( \mathbf{r} \cdot \mathbf{r} \right) ^{\frac{1}{2}}
$$
Therefore
$$
\begin{align*}
\dot{r} = \frac{\mathrm{d}r}{\mathrm{d}t}
&= \tfrac{1}{2} \left( \mathbf{r} \cdot \mathbf{r} \right) ^{-\frac{1}{2}} \frac{\mathrm{d}}{\mathrm{d}t} \left( \mathbf{r} \cdot \mathbf{r} \right) \qquad \: \textrm{(chain rule)}\\
&= \frac{1}{2r} \left( \frac{\mathrm{d}\mathbf{r}} {\mathrm{d}t} \cdot \mathbf{r} + \mathbf{r} \cdot \frac{\mathrm{d}\mathbf{r}}{\mathrm{d}t} \right) \quad \textrm{(product rule)}\\
&= \frac{\mathbf{\dot{r}} \cdot \mathbf{r}} {r}
\end{align*}
$$

 

[PeroK]

$$
r = |\mathbf{r}| = \left( \mathbf{r} \cdot \mathbf{r} \right) ^{\frac{1}{2}}
$$
Therefore
$$
\begin{align*}
\dot{r} = \frac{\mathrm{d}r}{\mathrm{d}t}
&= \tfrac{1}{2} \left( \mathbf{r} \cdot \mathbf{r} \right) ^{-\frac{1}{2}} \frac{\mathrm{d}}{\mathrm{d}t} \left( \mathbf{r} \cdot \mathbf{r} \right) \qquad \: \textrm{(chain rule)}\\
&= \frac{1}{2r} \left( \frac{\mathrm{d}\mathbf{r}} {\mathrm{d}t} \cdot \mathbf{r} + \mathbf{r} \cdot \frac{\mathrm{d}\mathbf{r}}{\mathrm{d}t} \right) \quad \textrm{(product rule)}\\
&= \frac{\mathbf{\dot{r}} \cdot \mathbf{r}} {r}
\end{align*}
$$

Hence, rather logically:
$$ \dot r = \mathbf{v} \cdot \mathbf{\hat r} $$

 

[Ibix]

If you are trying to reconcile this, @Martin68, note that there's a typo in @vanhees71's version - there should not be a dot over the $\vec r$ inside the square root.