Does SR seem like a total mystery to you?

[quantumdude]

Does SR seem like a total mystery to you?

This short book goes through relativistic mechanics and demystifies the so-called "paradoxes" of relativity clearly and concisely. Let's work through it!

http://www.physics.nyu.edu/hogg/sr/sr.pdf

 

[marcus]

printed out and looked thru the text

I printed out the text. It's good. I like the examples which are
many. And I like the diagrams---a lot of clear well-drawn (as far as i could tell) graphics. the math looks easy enough, so I would like to go thru this book with whoever else is going to.

One could do a lot worse than a 1997 text by a Princeton Institute of Advanced Study guy (hogg@ias.edu)

And it is less than 40 pages printed out! If you don't count the blank sides and the index. Piece of cake.

 

[RuroumiKenshin]

that's an excellent site! One teacher at my school is trying to understand SR and GR. I'll give him the address.

Anyhow, is there such a thing as "the dual velocity of special relativity"? I read the title in a book...

 

[rutwig]

Originally posted by Tom
This short book goes through relativistic mechanics and demystifies the so-called "paradoxes" of relativity clearly and concisely.

I have never found it a mystification. And texts like this one were written also many years ago (e.g. a short bouquin by Lev Landau).
It is a nice text, although many important references are missing in the final list.

 

[quantumdude]

*kick*

Anyone print the book out? Anyone want to go through it? SR is always a timely topic to cover here, as there is so much misunderstanding of it.

Originally posted by rutwig
I have never found it a mystification.

showoff...

 

[Mike H]

Tom,

Much thanks for the link, it looks like a very nice reference. I haven't thought much about SR in a while, it should be a good review.

Won't be able to go through it with the rest of you any time soon, but if you're still doing it over the summer I'll see if I can chime in.

 

[pmb]

Anyone print the book out? Anyone want to go through it? SR is always a timely topic to cover here, as there is so much misunderstanding of it.

Actually I don't have a printer and am having trouble downloading it at the moment but I'd be glad to discuss anything in relativity that you'd like to discuss. Anything in particular that you're interested in?

Pete

 

[ranyart]

Starter for one!

In the seventh page the author gives an overview of SR and Einstein's Principle, stating:A Sailor locked in a windowless room cannot even tell that wether the ship is sailing or docked.

This is a principle of Relativity, because it states that there are no observational consequences of absolute motion. One can only measure one's velocity relative to something else.

As Physicists we are empiricists:we reject as meaningless any concept which has no observable consequences, so we conclude that there is no such thing as "Absolute Motion." Objects have velocities only with respect to one another. Any statement of an object's speed must be made with respect with something else.

Ok so how does Nature interpret SR with repect to a particles position and its momentum? Take away the observer, and the particle must have 'some' knowledge of its position and momentum? Does the interaction of Observers invoke the HUP, or is it still valid for particles regardless of Observers?

If as the author says that particles have respect to other particle's position and momentum(relative), then the HUP principle is invalid? if particles interact, then any interaction will have to be a precise interaction without observers. Take away the observers and particles interact by their precise knowledge of where in space and time they, and their interacting partners are. Take two particles(A+B), A particles speed is made with respect to another particles(B) position?, with the other particle (B) position relative to particles (A) momentum, they are equivelent, and consequently cancel out!

A sub-atomic particles speed, with respect to another sub-atomic particles speed would be meaninless, they would be not measuring with respect to anything! without observers?, and yet observers change Nature with respect to HUP?

 

[marcus]

Originally posted by Tom


...This short book goes through relativistic mechanics ...Let's work through it!

http://www.physics.nyu.edu/hogg/sr/sr.pdf

To start working thru it, here is problem 1-1

You are driving a steady 100 km/h and at noon pass a parked police car which at 12:20 passes you at a steady 120 km/h.

After 1/3 hour you have gone 33 and 1/3 km
And so has the cop, so he has driven for 5/18 hour.
It takes that long for him to catch up, closing at 20 km/h.
So the separation the cop had to close, at 20, for 5/18,
is 5.55555 km-----5 and 5/9 km.

(a) It is moving 20 km/h relative to you
(b) Cop started driving at just after 12:03
Say at 12:03:20
(c) He was 5 and 5/9 km from you when he started.

Warning this may contain an error. Very easy to make careless errors in this sort of thing so would
appreciate if you'd confirm and do the next one. I will reciprocate by checking your work if you wish.

 

[marcus]

Originally posted by Tom
Does SR seem like a total mystery to you?

This short book goes through relativistic mechanics and demystifies the so-called "paradoxes" of relativity clearly and concisely. Let's work through it!

http://www.physics.nyu.edu/hogg/sr/sr.pdf

My impression is that there is of late a near-consensus in physics about what mass is and that this textbook conforms to it---see section 6.4.

The consensus is that mass is inertia and that inertia is a force/acceleration that does not depend on the direction of the force. Moving bodies do not have inertia in that sense (the realization goes back to 1904). So the mass of a particle is defined as its inertia at rest. Something like a photon, which cannot exist at rest, has no inertia and hence zero mass.

The author of this 1997 textbook deprecates the outmoded concept of "relativistic mass" which, to the extent that it is applied to moving bodies, is not a well-defined inertia.

Is this controversial or not? I had assumed for some time that it was not controversial and that the "relativistic mass" notion had finally been laid to rest.

Does anyone know of a more recent (post 1997) textbook in SR that does *not* define mass as rest mass? I would guess that most reputable texts treat it the way this one does.

Pages 30 and 31----on 4-momentum, rest mass, and conservation laws----are especially relevant. Also compare the Usenet Physics FAQ page on mass

http://math.ucr.edu/home/baez/physics/Relativity/SR/mass.html

Incidentally this page has an quote from a 1948 letter by Einstein advising against the use of the "relativistic mass" concept.

 

[quantumdude]

Originally posted by pmb
Actually I don't have a printer and am having trouble downloading it at the moment but I'd be glad to discuss anything in relativity that you'd like to discuss. Anything in particular that you're interested in?

Pete

I know Special Relativity, but I wanted to get something going based on a primer, because SR is the most popular target among internet loonies, including those that troll PF. Better to innoculate the populace against that kind of thing than combat each and every crackpot that comes along, I say.

 

[quantumdude]

Originally posted by marcus
The author of this 1997 textbook deprecates the outmoded concept of "relativistic mass" which, to the extent that it is applied to moving bodies, is not a well-defined inertia.

Is this controversial or not? I had assumed for some time that it was not controversial and that the "relativistic mass" notion had finally been laid to rest.

Does anyone know of a more recent (post 1997) textbook in SR that does *not* define mass as rest mass? I would guess that most reputable texts treat it the way this one does.

I don't know of anyone who talks about "relativistic mass" anymore. It's a bad idea that serves only to confuse. For instance, in the EM Lagrangian, there is no 'mass term' at all, but using "relativistic mass" forces us to say that light has some kind of "equivalent mass" based on its energy.

I'd like to back this up to Chapter 1, in case anyone else is interested. Later, I'll look at your work on that problem you did.

 

[marcus]

Originally posted by Tom


I'd like to back this up to Chapter 1, in case anyone else is interested. Later, I'll look at your work on that problem you did.

Problem 1-2 involves drawing pictures which I cannot do (my computer skills are rudimentary).

Problem 1-3 says you throw a superball at speed v towards a wall that is moving towards you at speed w. Perfect bounceback. What speed does it come back to you with. Consider the limit for large w.

This is classical, we haven't got relativity yet. From the wall's point of view, the wall sees the ball coming v+w at it. The wall reflects it back with v+w speed.

So from your viewpoint the ball is coming back at you with v+2w
speed.

If w is much larger than v then one can neglect v and just say that to a good approximation the ball's speed is 2w.

Problem 1-4
a) 26.6 degrees south of east
b)1.12 meter per second
c) 30 degrees north of east
c) 0.866 meter per second

Your idea is to start at Ch 1 and roll thru? Sounds good to me.
Like the author's style and only 60 pages in all. Initial problems of course are trivial. More people working them the faster it will go
but even for one or two people its no big deal.

 

[quantumdude]

Notes on Section 1.1

Marcus,

Sorry for the late reply--I've been busy. Hope you're still with me, and hope that some others will jump in.

I agree with your solutions, but I would like to present them in a different way. Specifically, I want to carefully specify both reference frames and events. This is not necessary for the Galilean problems, but it will help tremendously with the special relativistic problems later.

First, I want to flesh out a few details missing from the text.

1.1 What is a Principle of Relativity?
Galileo's principle of relativity states that inertial observers cannot determine their state of motion without making reference to the outside world. That is, the notion of "absolute motion" has no meaning, as it has no observable consequences. Thus, we only speak of relative velocities.

Denote "the velocity of A as measured by B" as "v_AB", subject to the following two laws:

1. Galilean velocity addition: v_AC=v_AB+v_BC
2. Reciprocity: v_AB=-v_BA

edit: #1 is sometimes called the composition of velocities.

The specifics of Galilean relativity are, for a stationary^* observer S and an observer S' moving with speed v_S'S along the +x axis are:

x'=x+v_SS't=x-v_S'St (last step by reciprocity)
t'=t

where unprimed coordinates are measured by S and primed coordinates are measured by S'.

(^*Of course, I do not mean that S is absolutely stationary. What I mean is that we are working in the rest frame of S.)

 

[quantumdude]

Problem 1-1

Problem 1-1:
You are driving at a steady 100 km/h. At noon you pass a parked police car. At 20 minutes past noon, the police car passes you, traveling at 120 km/h.

a.) How fast is the police car moving relative to you?
b.) When did the police car start driving, assuming that it accelerated from rest to 120 km/h instantaneously?
c.) How far away from you was the police car when it started?

Solution:
Frames of reference:
*Ground (S)
*Me (S')
*Police car before it starts moving (S, same as the ground)
*Police car after it starts moving (S'')

The velocities in the problem are:

v_S'S=100 km/h
v_S''S=120 km/h.

Coordinates (x_i,t_i) given in units of (km,hr). The fact that they are unprimed indicates that they are measured relative to the ground (S). Let the origin of coordinates in S be the point at which I pass the police car at 12:00 noon.

Event 1: I pass parked police car. (x₁,t₁)=(0,0)
Event 2: Police car starts moving. (x₂,t₂)=(0,?)
Event 3: Police car passes me. (x₃,t₃)=(?,1/3)

a.) This is looking for v_S''S'. I can relate this to the known velocities by Galilean velocity addition:

v_S''S=v_S''S'+v_S'S
v_S''S'=v_S''S-v_S'S
v_S''S'=(120 km/h)-(100 km/h)
v_S''S'=20 km/h

b.) This is looking for t₂. One way to get it is to use what I know about v_S''S and v_S'S.

v_S''S=(x₃-x₂)/(t₃-t₂)
v_S'S=(x₃-x₁)/(t₃-t₁

The only unknowns above are x₃ and t₂, the target of the problem. Using v_S'S to eliminate x₃=v_S'St₃, I get for the expression for v_S''S:

v_S''S=(v_S'St₃-x₂)/(t<sub>3-t2).

Solving for t2 (tossing out all zero coordinates) yields:

t2=t3(1-vS'S/vS''S)
t2=1/18 h, or 3 min 20 sec.

That corresponds to a clock time of 12:03:20.

c.) This problem is asking for x2'. Note the prime!

Since I already know x2, I can use the Galilean transformation:

x2'=x2-vS'St2
x2'=0-(100 km/h)(1/18 h)
x2'=-5.6 km

So the police car was 5.6 km (rounded) away from me when it started.</sub>

 

[quantumdude]

Problem 1-2

Problem 1-2:
You are walking at 2 m/s down a straight road, which is aligned wiht the x-axis. At time t=0s you sneeze. at time t=5s a dog barks, and at the moment he barks he is x=10m ahead of you in the road. At time t=10s a car which is just then 15m behind you backfires.

a.) Plot the positions x and times t of the sneeze, bark and backfire, relative to you, on a 2D graph. Label the points.
b.) Plot positions x' and times t' of the sneeze, bark and backfire, relative to an observer standing still, at the position at which you sneezed. Assume your watches are synchronized.

Solution:
Frames of reference:
Me (S)
Dog-Car-Other Observer (S')

The velocities in the problem are:
v_SS'=2 m/s

Coordinates (x_i,t_i) are given in units of (m,s}.

Event 1: I sneeze. (x₁,t₁)=(0,0)
Event 2: Dog barks. (x₂,t₂)=(10,5)
Event 3: Car backfires. (x₃,t₃)=(-15,10)

a.) Since we can't plot graphs here, we will have to be satisfied with writing down the ordered pairs. For part a.), they happen to be just as I wrote them down above.

b.) This is asking us to look at the same 3 events, but from the point of view of S'. For this we can use the Galilean transformation:

x_i'=x_i+v_SS't

to get:


(x₁',t₁')=(0,0)
(x₂',t₂')=(20,5)
(x₃',t₃')=(5,5)


edit: typo

 

[schwarzchildradius]

I printed out some of the text and will participate, if I may, just not this evening. SR is still mysterious, yes!

 

[marcus]

Tom, I agree with your wishing to have a systematic format, using explicitly stated reference frames. Though the answers I posted to 1-1, 1-3 and 1-4 were very informally stated, for quickness of typing mainly. Also I like the idea of posting the answer in blue so one can cut to the chase---making the bottom line stand out.

I want to compare our answers. I said

(a) It is moving 20 km/h relative to you
(b) Cop started driving at just after 12:03
Say at 12:03:20
(c) He was 5 and 5/9 km from you when he started.

And you said

(a) v_S''S'=20 km/h
(b) That corresponds to a clock time of 12:03:20.
(c) So the police car was 5.6 km (rounded) away from me when it started.

So we agree on that one---modulo my lazy writing style. I actually liked the problem with the cop. And he has some nice spaceship sitcoms too which we will get to ere long I reckon. I appreciate that you are busy (with realworld grad student or postdoc or teaching demands) and am not at all impatient. Please do not
shortchange the realworld stuff for PF tutorials! Also we must I suppose share problems so I will leave 1-5 and 1-6 for whoever else shows up and have a look at problem 1-7

Originally posted by Tom
Problem 1-1:
You are driving at a steady 100 km/h. At noon you pass a parked police car. At 20 minutes past noon, the police car passes you, traveling at 120 km/h...