

Ask HN: What are physicists doing? - cool-RR

In this thread I would like to consult with you, HN readers, about a problem I have with physics. It is a sort of gap between the way I research physics, and the way mainstream physicists do it. This thread will probably appeal only to those of you who are interested/knowledgeable in physics.<p>A little introduction about myself is necessary.
I'm 22 years old. I live in Israel. My main occupation right now is studying physics. However, I am not a student in a university, nor am I affiliated with any other kind of academic institution. It's been about a year and a half since I've started studying physics in this independent way. I used to be an official student, a few years ago. I was an undergrad in Electric Engineering. I quit there after one year. Then I decided to start studying math independently. I did that for about a year and a half. Then I stopped with math and decided to start studying physics, with the goal of figuring out how the universe works.<p>So I'm about a year and a half into my quest. I can say that up to now I studied Special Relativity and Classic Electromagnetism.<p>The thing is, I feel that I have diverted from the ways of academic physicists. Actually, after these 1.5 years it has come to a point where I feel like I'm speaking a different language than the one they're speaking. Perhaps I took a wrong turn somewhere and I'm heading into a dead end? Perhaps the mainstream physicists took a wrong turn and I'm taking the right one? Or maybe some other possibility? I am hoping that you, HN readers, will be able to shed some light on this gap.<p>What are these differences between me and them? It will take some exposition before I could explain. Some of the things I say about physics may seem wrong or provocative to you. If you feel the urge to tell me I'm wrong, please do it with a thorough, logical argument. If anything seems unclear, please ask. Here we go:<p>In Newtonian mechanics, life was simple. There was a collection of bodies in different places. Each pair of them exerted forces on each other. There were rules that said exactly how much force they exerted. With these rules it was possible to calculate exactly what the force on each body was. After you knew the force for a body, you could know the acceleration that that body would have, according to the revered formula, F=m a, or in its more useful form, a=F/m. After you knew the acceleration, you could advance the simulation by a small time-step. The bodies would then move a bit, and you would calculate the forces again, and so on.<p>If you took a small enough time-step, you could calculate the outcome of any physical system to any desired accuracy. All the subjects taught in Newtonian mechanics, such as angular momentum, centrifugal forces, conservative fields, and kinetic and potential energies would appear as emergent phenomena from these rules. They were just epiphenomena to the true axioms of physics: The force equations and F=m a.<p>That was Newtonian mechanics. In approaching Special Relativity, I expected the same style, maybe a bit more complicated. Eventually that's what I got, but it was hard work, and I had to build big parts of the system myself, with only hints from physics textbooks (more about that later.) It turns out that Special Relativity is just a tad more complicated than the above description of Newtonian mechanics. Instead of the formula a = F/m, there is a more complicated formula:<p>a = (F- v (F v)/c^2)/(m gamma)<p>(Where v is the velocity, gamma is some function of the velocity, c is the speed of light and that (F v) is a dot product.)<p>And the formulas for calculating forces become more complicated as well. I will not list them here, since the mathtext will become too cumbersome, but if anyone will insist I'll post them. These equations are eventually what is called Classic Electromagnetism. All the revered Maxwell equations turn out to be just special cases of these equations.<p>(Also, in Special Relativity there is the issue of Lorentz transformations: but that is important only if you want to change viewpoints, and even then it can be deduced from the rules above.)<p>Another note: I know that the system I described is not an end-all model of the world. It does not include Quantum Mechanics, and thus it will be valid only for macroscopic bodies. (It also does not include General Relativity, and thus it could not deal with gravitation, but that is less important in my opinion.)<p>I mentioned that I had to build most of that system myself, and that physics textbooks don't give this system explicitly. That is the biggest gap between the physics community and myself. Physicists do not seem to accept this system. The equation for the acceleration that I supplied above cannot be found in any textbook, or at least I didn't find it. That is even though it can be easily derived from known equations of Special Relativity. The equation for the Electromagnetic force is almost as hard-to-find, although it can be derived from the well-known Liénard-Wiechert potentials. Why are these things not mentioned in textbooks? Am I blind to something? What are physicists doing, how can they research anything without knowing this system?<p>About Quantum Mechanics: Even though the system I described will break down at the quantum level, I think it's indispensable for trying to figure out how the quantum world works. It is true that as you go smaller and smaller, the physical reality will deviate from this macroscopic model; But if you want to study and understand these deviations, you should understand the macroscopic model first, so you will know exactly what to compare the physical reality against!<p>That's my opinion. I may be wrong, and if I am, I would love to hear a well-reasoned rebuttal. I really hope you guys can shed some light on this.<p>Ram.
======
nsrivast
You say "physics textbooks don't give this system explicitly". They don't need
to - they simply present the system that's most instructive to learn or is
most interesting to their authors. As long as your formula or "system" is
consistent with the accepted formulations of special relativity, you have no
reason to worry.

PS - Most physics communities are getting by with their own methods, and if
you really think yours adds something you should write a textbook (or a
paper).

~~~
cool-RR
I understand that their systems may be simpler for their uses, and it's
possible that for this reason they use Maxwell's equations and things like
that: But how can they not mention it, even once? I would personally expect
these equations to be revered in every Classic Electromagnetism book. Okay, so
they are not revered, maybe my taste is a little peculiar, but they are not
even mentioned! I just can't understand it. Think how much Maxwell's laws are
revered, and this is one formula that contains them all and more, in one line.
Don't you think that they would mention it?

That's what's baffling me. Do they not know this? Do they not care? How can
they not care?

About your PS: Yes, I'm working on writing this.

------
newt0311
So... Special relativity is called "special" because it specifically assumes
_no acceleration_ and therefore, no force. That formula you have is an
approximation for "small" forces. General relativity is what actually explains
space with acceleration (using Riemann Geometry, another fascination and
extremely complex topic in of itself relying on tensor calculus, which is
_another_ fascinating and extremely complex topic in of itself). Secondly, the
Lorentz transformation is _critical_ to special relativity, because that is
what gave rise to the entire theory and also because the Lorentz
transformation is exact (up to QM effects and 0 acceleration). Also, the
Lorentz transform is sufficient to derive the result e = mc^2 among many other
useful results on momentum and particle collisions (or at least the
aftereffects thereof, since we can have no forces) which is why special
relativity is even taught in isolation.

As to the textbooks, all I can say is that you haven't come by the right
textbooks yet. I would advise reading the Feynman's lectures on physics (all 3
volumes). Expensive but worth it and if you want, you could probably find free
pdfs online. FLs does indeed go into the gory details of special relativity
(v1 I think) and even shows how to derive most of the useful results including
(I think) information on how to derive the Lorentz transformation from the
Special Relativity's base assumption: the speed of light is constant in all
time frames. ENM along with several applications is also discussed in FLs (v2
I think). FLs V3 covers QM is great detail (well... the parts that we humans
can solve mostly). Another very good book on ENM would be Electricity and
Magnetism by Purcell, Berkley Physics Course Vol. 2.

Oh btw. the central assumption of General Relativity is that force and gravity
are just 2 different manifestations of the same phenomenon. Thus, for very
weak gravitational fields, you could actually use the formula you have. Just
that it would not be very useful because a) you would have to interpret it as
constantly changing time frames over small time intervals, and b) because I
don't think the Earth's gravitational field (or the moon's) is weak enough to
justify the approximations inherent in your equation.

A note on finding good textbooks: Pick a good university. Any good university
(I would advise Caltech but thats because thats where I study) and chances are
_very_ good that said universities will publish the course textbooks for their
classes. Some will even publish the homework assignments and solution sets
along with lecture notes. Eg.
<http://www.pma.caltech.edu/GSR/physicscourses.html> is the place where CIT
has currently placed a convenient listing of all the physics courses offered
with links to their web pages which contain among other things: the textbooks,
syllabus, and in most cases, the homeworks for the class. Finding textbooks
from there shouldn't be very difficult.

~~~
cool-RR
There are many objections I have to raise to your post. But let's just look at
the first thing you say.

You say that SR can't handle acceleration. I disagree. Let's examine this
issue.

My first question about it is: Assume you have a "twin paradox" situation. One
twin stays on earth for a year, while the other twin goes somewhere far away
in space and returns, in relatvistic speed. The travelling twin accelerates
smoothly in his journey. Given the twin's trajectory, the mission is to
calculate in how many years he has grown old. Do you think that SR can't
handle this case?

Second question. Observe the Lienard-Wiechert potentials. They say the exact
value of the EM field at any given point. What is the significance of the
value of the field E, if not the chrage of the body times the force that acts
on it? If it does mean that, then "force" in which context, if not SR?
Newtonian? GR?

~~~
newt0311
The twin paradox cannot be handled by SR. The difference in aging comes about
due to time dialation caused by the differential acceleration that the twins
experience (the twin in the spaceship is accelerated and the other is not). SR
can be used to judge the middl period after the acceleration but it will not
give any useful information because you can always switch viewpoints. If you
have two bodies moving at some relative velocities, _both_ can claim that the
other is moving slowly in time. The mathematics of communication and speed of
light work out so that this system is consistent. The difference in measured
time comes from the acceleration that one of the bodies must undergo to enter
the same time frame as the other.

Secondly, electric fields have intrinsic effects as in EM radiation
(colloquially known as light) and need not apply any force to have effects.
The movement of emitters of electrical fields through space and acceleration
thereof actually give rise to magnetic fields. Read Berkley Phys. Vol. 2 ch. 5
which shows how this happens in the framework of SR. It later hints how
tensors can be used to generalize this result to GR. So... in response to your
question, if force is applied, either it must be approximated in a Newtonian
or SR context, or GR must be used in its full generality. Usually, the forces
and particles involved are sufficiently small that approximations work (see
success of Newtonian mechanics), but that is not the general case. Also, very
common is the tendency to derive general results and then use them is special
cases. Maxwell's equations are an excellent example. They refer only to EM
fields and are exact (uptil QM of course).

~~~
cool-RR
Okay Newt, now we have something we can compare! Because I claim that SR _can_
handle such a case. I propose that I will give the answer as I calculate it
from my version of SR, and you can give it from GR or whatever you think is
necessary. Does that seem like a worthwhile comparison to you? Let's say that
our travelling twin takes a trip of one second (not one year, to make the
calculation easier). Let's say he goes in the following trajectory: x(t)=0.9 c
sin (k t) /k Where k equals (pi/second). How older will the twin be after the
journey? I got the result of 0.7459255 seconds. What is yours?

~~~
newt0311
There is a problem with your analysis. Switch viewpoints to the reference
frame of the traveling twin. In that case, that twin stays in a constant
position and the other twin travels with a trajectory of x(t) = -0.9 c sin(kt)
/ k. The negative sign is irrelevant as we are only interested in absolute
velocity and the negative sign implies that the movement is in the opposite
directions. Then by your calculations, the other twin should now experience
0.74... seconds. Ie. Without accounting for the acceleration that one of the
twins experiences, you can always switch frames and therefore cannot draw any
conclusive results for both twins simultaneously unless you fix the reference
frame (but in that case, differential aging really makes very little sense).

As to calculation the actual difference in age, I don't know GR sufficiently
well to be able to calculate the aging of the twins but I know some people who
do. I have contacted them and will get back to you once they send me an
answer.

~~~
cool-RR
Hello Newt,

Thanks for answering and for forwarding this to people who know GR, this might
really help me.

Regarding your first paragraph: I didn't give you my analysis, I only gave you
a final answer, so how can you say there's a problem with my analysis? It's
more like, there's a problem with your guess of what my analysis was. I
phrased the original question accurately and gave a final answer.

The contradiction you're talking about does happen if you try to switch
reference frames without taking note of the acceleration. I didn't try to
switch reference frames.

~~~
newt0311
That is the problem. One of the central tenants of relativity is that what
reference frames we choose is irrelevant as long as we account for all the
relativistic effects. In you analysis, whatever that may be, you have two
twins which separate, move around, and then return to the same reference frame
and your result is apparently dependent on which twin's reference frame you
are using. That is a contradiction. Thus the need to account for the
acceleration that one of the twins experiences w.r.t. the rest of the
universe.

~~~
cool-RR
We are having quite a funny argument, because it seems we both see the
problem.

"One of the central tenants of relativity is that what reference frames we
choose is irrelevant as long as we account for all the relativistic effects."

I think that applies only to _inertial_ frames. At least in my version of SR
that is so.

"your result is apparently dependent on which twin's reference frame you are
using. That is a contradiction."

I know it is dependent. I don't see what's the contradiction. The earth twin
has a special status - he is non-accelerating. His reference frame is
therefore inertial. The other twin _is_ accelerating. His reference frame is
non-inertial.

Where is the problem here?

