Questions about light (special relativity)

It's been many years since I took college physics, and find that I no longer really understand relativity. Got a question that I think most of you can answer:

Let's say there are beings that live on a comet. This particular comet goes very fast, but don't focus on that, because in any case the beings on the comet have clocks that are accurate within billionths of billionths of seconds, just like we have on earth. Or, in other words, even if not at relativistic speeds, the comet beings and humans can measure small time distortions. If you'd rather imagine a comet moving at .05c so the time distortion becomes more obvious, that's fine.

Now relativity tells us that with velocity, the sense of time changes. However, in this case, both the comet beings and humans on earth believe that they are the ones at rest, and it's the other that is moving in relation to it.

So, the questions:
1 - If both human and comet beings start sending out signals that represent clock ticks (the signals are radio signals moving at light speed, but carry the clock tick information), will each group of beings see the other's clocks as moving slower, since they each feel that the other is moving relative to them?

2 - This kind of precedes question 1, actually. Does the presence of the strong gravity field of the sun or anything else actually arbtirate the "who is in motion" question? If the answer is yes, I'd like to rephrase the initial conditions a bit.

3 - What happens if someone from the comet blasts off in a rocket headed towards earth? Assume again the rocket sends out signals that carry information on clock ticks, which can be received on earth and on the comet. I think the answer is: since the rocket is accelerating away from the comet, the comet beings see the rocket's clocks slowing down. On earth, the rocket seems to be decelerating towards earth speed, not accelerating, so the rocket's clock seems to be speeding up. The being on the rocket knows he is accelearting away from the comet, so he agrees with the comet people that his clock is slowing down relative to theirs, and agrees with the earth people that his clock is becoming more in sync with theirs (i.e., his clock is slowing to match earth clocks, although on earth we think his clock is speeding up to match earth clocks).

Thanks!

are you stoned?

Edit:
*lol*!

Is the comet headed for us or away from us?

Blinded: sure, I'm feverish and incoherent on cold medicines. But then, you knew that /ubbthreads/images/graemlins/smile.gif

GJW: INteresting question -- I can't see how it matters, relative velocity is relative velocity. But, if you think it makes a difference (I'd like to hear why, if so), I'd like to hear answers from both points of view, headed towards and away.

BTW, a re-phrasing of question 3: I think the comet people see the rocket's clock slowing down and becoming more in sync with earth's slow clocks. The earth people see the rocket's clock speeding up to catch up to earth's clocks. And the rocket thinks his clock is slowing down compared to the comet's, and becoming more in sync w/ earth's slow clock.

I recall from modern physics that if someone travels away from the Earth and then returns, they will have aged less. There is apparently a distinction between just traveling away, and traveling away and returning. Unfortunately, it was about 15 years ago for me, and I just can't remember what it is.

Also, I don't think it has anything to do with gravity. There is another type of time dilation effect called the gravitational time dilation effect, but I think this topic is explainable within the confines of special relativity only.

Lux, ya like 19 years for me. You remember correctly, I think,but the distinction is not travelling away or returning -- it's accelerating and velocity. Once you accelerate to high velocity, there's no longer any question of who is relatively at rest or in motion. You've accelerated, so you're in motion, so your clock runs definitively slower than an earth clock, proportional to your velocity. By accelerating, general relativity speaking you've given up your ability to claim that you are at rest. Your clock will run relatively slower than an earth clock regardless of whether or not you come back. That's why I introduced the beings on the comet -- they have every reason to claim that they're the ones at rest and that the earth is whipping past them, rather than vice versa.

Acceleration and gravity are, to my knowledge, indistinguishable in relativity, although again I could have this wrong. In fact, acceleration and gravity can be indistinguishable period, right? Go out in space and start accelerating at 10m/s/s, and you'll feel exactly as if you're in earth gravity. Go in a plain and free-fall, and you'll feel exactly as an astronaut under zero gravity feels (well, at least 'til you hit the ground /ubbthreads/images/graemlins/smile.gif Acceleration kicks in relativity effects like relatively slower clocks just like gravity warps spacetime and causes relativity effects like relatively slower clocks (which has been verified experimentally).

All of this should be prefaced with "I think". If I were sure, I wouldn't be asking /ubbthreads/images/graemlins/smile.gif

Yeah, I'm pretty sure gravity and acceleration are indistinguishable. This is a consequence of different masses falling at the same rate. There's no other reason why the gravitational mass and inertial mass should happen to be same. I presume this is what lead Einstein to view gravitational effects as not being due to a force, but due to the local warping of spacetime.

As for the rest your problem, I don't remeber the stuff too well. Maybe I should take Blinded's suggestion. That might jog my memory. /ubbthreads/images/graemlins/grin.gif

Uhh, the bus drivers name is Bob!

Actualy, as I understand it, the theory of realtivity is not what is involved here. The relativity in it's most basic form says that physics as we understand them here apply everywhere. For example, If you hit a tennis ball with a racket the ball flies in the oposite direction. This is physics. The relativity means that it doesn't matter if you do here on some other planet, or a blazing comet, the same physics, or results occur. Therefore E=MC/2 is the same here as it is a billion miles in space, at any other speed, or any other environment.

Please correct me if I am wrong.

Joe,

You have asked some rather delicate questions, which actually can be broken down into simpler questions. Let's start with what, in relativistic physics, is called the "twin paradox" question.

This is the situation where two people are moving relative to each other at a large percentage of the speed of light, and the paradox is that BOTH of them think that the other's clocks are moving slower! How can this be? Well, it just is, and doesn't cause a problem until you start thinking of a situation where two twins start out on earth and one gets on a rocket and accelerates to .5 c and then we have this situation where they BOTH think the other's clocks are slower. Next the travelling twin returns to earth. Who should be younger? Well, the firm answer is that the one who went on the rocket will be younger, and this is because (and this is the most important thing in my entire response) special relativity applies ONLY to non-accelerated reference frames. Got that? So the twin who jumps in the rocket sure as heck accelerates, and so special relativity is not valid. It is only valid once he is up to speed (relative to the earth) and is no longer accelerating. Of course, most of these space trip ideas imagine a CONSTANT acceleration.

This brings me to the next "question", and to your statement above, which is 100 percent perfectly correct: acceleration and gravity are indistinguishable, not just in practice, but also in principle. This was Einsteins great insight, the one where he realized that you don't feel yourself falling, and which enabled him to formulate General Relativity, which is valid for reference frames that are accelerated relative to each other. But let's not get into that at the moment!

So, to answer your question no. 2, gravity does NOT select out a prefered rest frame, such as you have with sound waves. The rest frame is the frame which is not moving with respect to the air, when you're dealing with sound. But motion in the vacuum of space is ALWAYS relative. There is no prefered or absolute frame of reference.

Now, how about your third question? The guy in the rocket heading away from the comet towards earth sees BOTH earth's AND the comet's clocks moving slower, and likewise for them. Why? Because they are ALL in relative motion with respect to each other, right? Yet, the dude in the rocket actually goes from the comet and lands on earth, and HE is the one who "makes good" on the slower aging, as it were, because he is the only one who actually goes from one reference frame to the other.

Keep in mind that the light signals are travelling at the same speed no matter who's measuring them. What changes is the FREQUENCY. This may remind you of the "red shift". Time-space events change their respective relations depending on who's looking at them. In one system the time between "events" can be large and the distance small, while in another, the space can be large and the time short.

But acceleration is NOT relative. The guy in the rocket is seen to be accelerating by ALL reference frames. This is also why gravity is NOT relative. A black hole is a black hole in ALL reference frames. And this is the solution to the "twin paradox". We CAN distinguish between the twin who stayed on earth and the one who went to a star and back, because he's the one who felt the acceleration. Similarly, rotation is NOT relative. A spinning bucket is seen to be spinning by ALL observers. Of course, this inspires all sorts of questions such as "if the only thing in the universe were a spinning bucket, how would you KNOW whether it was spinning or not because there's nothing to reference it to?" Well, exactly. It is IMPOSSIBLE for the only thing in the universe to be a spinning bucket, because mass, gravity, and space-time are all connected. If you have only a spinning bucket you have no, are almost no space and time, because you have almost no mass. So gravity DOES select out an absolute standard for acceleration.

As for the relative clocks stuff, the short answer is that acceleration is outside the scope of special relativity and that it also resolves the paradox.

If you do a search on "relativity" here in the cafe, or look through my posts in the cafe, you will find other, equally scintillating answers to questions such as yours. If you still have questions, PM me.

Jim, fantastic answer, which I'll have to ponder a bit more. I'll also seek out your other posts. It looks like I kinda sorta have a basic elementary grasp on things, shockingly enough /ubbthreads/images/graemlins/smile.gif Thanks!

Joe

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Bravo25 said:
Uhh, the bus drivers name is Bob!

Actualy, as I understand it, the theory of realtivity is not what is involved here. The relativity in it's most basic form says that physics as we understand them here apply everywhere. For example, If you hit a tennis ball with a racket the ball flies in the oposite direction. This is physics. The relativity means that it doesn't matter if you do here on some other planet, or a blazing comet, the same physics, or results occur. Therefore E=MC/2 is the same here as it is a billion miles in space, at any other speed, or any other environment.

Please correct me if I am wrong.

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Okay, you're wrong /ubbthreads/images/graemlins/smile.gif heh, that felt good to say. Seriously though,special relativity is about perceptions of spacetime when bodies are at constant velocity versus each other (thanks for the remind JS!), and general relativity pulls gravity and acceleration into the mix. It's special relativity that says that if you and I are passing each other at relativistic speeds, each of us will think the other's timeframe is running slow, and that we may witness the same events but see them happening in different temporal orders.

It may also be the case that relativity has something to say about what you mentioned -- the truth of physical laws regardless of your position in spacetime -- but I dunno. In fact, and here I'm way out of my league, I thought I read somewhere or other that some physicists are looking at the possibility that physical laws were different early after the big bang (I don't mean just that all forces were united, etc., I mean the laws governing them were different than we'd expect by just working backwards from the laws we know about), but I don't believe that that is the accepted view.

Joe

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It may also be the case that relativity has something to say about what you mentioned -- the truth of physical laws regardless of your position in spacetime -- but I dunno.

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There are two postulates from which the Lorentz transformations can be derived--these are the equations which tell you how an event in space-time (x,y,z,t) will transform when seen by a moving (non-accelerating) observer, i.e. (x',y',z',t'). The "normal" transformation equations are simple, and are called Galilean. They are simply found by adding the relative velocity, and by assuming that watches run the same, i.e. t=t' regardless of relative motion.

Anyway, the two postulates are as follows:

1. The laws of physics are the same for all non-accelerated reference frames. That is, we don't need to add any correction factors or terms depending on which reference frame we are in. The people on the comet would find the same laws of motion and electromagnetism, etc., as the people on earth.

2. All observers, regardless of their relative motions, measure the same speed for the speed of light, namely 186,000 miles per second.

Using these two starting points, you can derive the mathematical statement of special relativity.

And on that note, I should emphasize that mathematics is the ONLY language which can accurately embody physics. Any description in words is ambiguous at best, no matter how intriguing. Still, any good physicist will be able to explain this stuff to the lay person in terms he or she can understand.

And yes, many physicsts have toyed, or are toying with the possibility that the laws of physics change with TIME, albeit very slowly. Personally, I think this is a dead end, and sort of complicated and ugly given the relative nature of time. It would be like saying the something changes with distance. Huh? What distance? Whose distance? From what to what? Of course, the big bang does give you a very definite starting point from which to measure this zero time, but from there it gets messy in a hurry.

To my mind, the big issue in physics today is how to mesh General Relativity with Quantum Mechanics, or quantum chromo dynamics (QCD) because they have a fundamental philosophical disagreement over the nature of time. GR sees time like a rug. There it is: future, present, past - just like the strands of the warp and woof in a rug. No uncertainty, in principle. QM and QCD, however, tell us that the future is FUNDAMENTALLY uncertain, not just in practice, but in principle, which is why QCD is so dang hard to interpret, with negative probabilities and balancing infinities, and other questionable mathematics. P.A.M. Dirac lamented the mathematical base of what is now known as the standard model and renormalization procedures (essentially dividing infinity by infinity! and inserting what you know is the answer, mass of the electron or whatever).

Gravity is even more of a problem because it is so very very weak compared to electro magnetic forces that it is next to impossible to study on the quantum level.

Ok. </RAMBLE> Enough.

Actually, what reminded me of all this is because I'm reading a book written for laymen on superstring and M-theory. I think it's called The Elegant Universe. The beginning sections on relativity made me realize how much I'd forgotten.

Actually, I can think of a whole batch of string questions, if you understand it, Jim, and are willing to keep answering!

Joe

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Joe Talmadge said:
Actually, I can think of a whole batch of string questions, if you understand it, Jim, and are willing to keep answering!

Joe

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This should be good. I have seen this batted around before, but I am always willing to learn something new. Go for it.

Okay, hopefully Jim is still listening!

The overall question is, how does superstring theory unite gravity and quantum mechanics. First, let me state what I think the problem is.

For gravity, spacetime -- more specifically, space -- is smooth. This is fine for "large" regions of space.

Okay, let's head off to quantum mechanics for a second.The heisenberg uncertainty principle tells us we can't be sure of energy of a particular area of space, if we are looking in a small enough time period. The smaller the area of space and the shorter the time period, the less we can be sure that an "empty" area of space is really empty. An empty area of space can suddenly have some energy, and then release that energy again, as long as it does so quickly enough that nature doesn't notice. And, since energy and matter are convertible currencies (E=mc^2 tells us how one can become the other), a quantum energy fluctuation can simply transform into a particle and an anti-particle, which then must re-combine to become energy again within the heisenberg limit. Again, nature lets something come from nothing, as long as it returns to nothing again quickly enough. In fact, as you look into smaller and smaller places and in shorter time durations, heisenberg uncertainty says that there must be energy fluctuations. So as we look into a smaller enough piece of spacetime, we see an area of space that is actually churning with energy fluctuations and particles appearing and disappearing. The smaller the area of spacetime, the more "quantum foam" we find.

So okay, we know that as we look at very small distances -- around the planck distance of 10^-34 meters -- empty space is really a roiling churning boil of activity. And we know relativity requires a nice smooth space for gravity. But since most relativistic physics is done over large distances and times, any quantum disturbances get smeared out and we can ignore them. But if we try to look at very very small areas (remember, on the order of 10^-34m) that have high gravity -- like the singularity at the center of a black hole -- then we are dealing with general relativity in a very small area that is definitely not "flat", but rather small enough to be filled with quantum foam.

Sanity check -- okay so far?

To summarize how I think string theory unites these two theories, I think that strings are on the order of the planck distance. And furthermore, strings are the smallest state of matter. That being the case, we more or less cannot probe anything smaller than a string -- smaller than the planck distance. This isn't a measurement problem, it's a statement about the nature of reality. Essentially, nothing under the planck distance is knowable -- or, to consider it another way, such distances don't exist.

I'm very shakey on that last paragraph, but what I'm essentially saying is that at the distance that quantum foam becomes a problem for general relativity, nothing is knowable anyway.

I'm sure I don't understand this right, but there it is.

Joe,

You as much or more about string theory as I do, and your statement of the basics above is probably better than anything I would have come up with.

You see, while I know the mathematics underlying special and general relativity and quantum mechanics--I actually took a course in general relativity and tensors and another course in differential geometry, and QM to the graduate level--I know absolutely nothing about the mathematical statement of string theory, and without that I am lost. My current project, which I haven't really gotten started on, is to understand relativistic QM, or QCD as it is sometimes called.

Don't get me wrong, it's still fun to think and talk about such things, but trying to expound upon matters of physics without the mathematics is like trying to understand a drama staged in a foreign language. You can tell when people are angry or sad or in love or fighting or running, but you don't really understand the details. Unfortunately for people like me, those sorts of topics such as string theory or quantum cosmology or white holes or alternate universe theories, and so on, are what most people want to know more about. Granted, it's exciting stuff, but I might as well have a background in Renaisance Literature, because it's WAY out of my league. My thesis advisor and I both had a massive black book titled "Gravitation" by Kip Thorne, Charles Misner, and John Wheeler, about general relativity, and the book has "track 1" material and "track 2" material, the track 1 stuff being for a graduate student taking a course in GR. My thesis advisor, Dr. Kenneth Brownstein, who is perhaps the smartest physicist I personally have ever met, said that the only people who really understand the track 2 material are the people who wrote the book! After that I sold that particular book on GR, as I seriously doubted whether or not I'd ever work through it. Some of my fellow grad students joked that it made a great paper weight.

What I'm trying to say is that there are very, very few people out there who can speak intelligently about something like string theory or quantum cosmology, or even relativistic QM. My graduate work was in QM and solid state physics, and I have made a special study of relativity, so I can and do speak on these subjects without too much fear of making an idiot of myself, but string theory? no *cough* way.

Joe; I think I am going to take "Jim's out" here. You have a much deeper grasp than I do. I had only considered that the existance of everything has root in mathemeatics, or is some how related to numbers. Since numbers, and math are infinite, I just assumed the reverse. Sub-infinite if you will, and thus never realy bought into the string theory.

Having said that, you will execuse me while i go remove my foot from mouth, and contimplate how little I really know on the string theory.

I do enjoy reading these though, and hope you will continue to post. Maybe my desire to learn is infinite as well, even my abilty isn't.

That's about the sum total of what I know, and I'm pretty sure it's not even right, particular on the string stuff.

I hear you on the requirement to understand the math. I looked at some of the equations, and it's pretty obvious that the math for superstrings is way way WAY beyond me even when I was stlil good at math as an engineering major. I could see the author trying to put superstring theory into words without the equations; he did amazingly well, considering. I mean, I almost kinda sorta have a grasp on 6-dimensional Calebi-Yao space transformations. Okay, maybe that's going too far /ubbthreads/images/graemlins/smile.gif But, I do understand why we're talking about Calebi-Yao transformations!

Interestingly enough, superstring theory is breaking new mathematical ground. Where previously it was always physicists running into problems, and then trying to find a mathematician who had solved it, now physicists are running into problems that no one has solved, and the mathematicians end up borrowing the physicists' solutions. Although to put it in computer terms, it sounds like physicist solutions are more like hacks, whereas mathematicians require elegant structured code.

Joe

In the unlikely event you found the above interesting, here appears to be some confirmation that I've got the general grasp of things (from http://www.astronomycafe.net/qadir/ask/a11103.html ):

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The topology of these compact manifolds may have certain symmetries associated with them which feed back upon the symmetries that we have uncovered among the physical particles themselves. In terms of calculations, treating particles as strings eliminates virtually all of the 'infinities' which have plagued earlier versions of quantum field theory such as quantum electrodynamics. These infinities emerged because the particles were assumed to have a point-like structure where field strengths may diverge to infinite values. In string theory, you only calculate properties of the particle that are greater than the quantum limit to space time at 10^-33 centimeters.

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The "manifold" discussed is a reference to 6-dimensional (7-dimensional in newer string theory) Calabi-Yao spaces. Calabi-Yao spaces are the way the "extra" dimensions of space, which are folded around themselves, are modelled.

One of the successes of string theory is that, whereas the standard model only recognizes the fact that there are three classes of fundamental particles which have such-and-such mass, etc., string theory explains the "why". The number of holes in the Calabi-Yao spaces determines the number of possible particle families; the way strings can vibrate in those spaces determines particle attributes such as mass and charge.

Joe

Oh great! Thats just great Joe. Just when I was starting to get a handle on the theory of relativity, and the biginning of physics, and even nano technology, you throw another wrench in the works. I can get my mind around somethings, but now you have me going off into a different tangent. You realize that now I am going to have to make time to read about QM, QP, and a midrid of other things that I am sure I don't yet comprehend.

I guess it is a good thing I enjoy learning about these things.