Gaining a Better Understanding of Special Relativity

[Urmi Roy]

Hi,

I've been doing the very basics of special relativity lately,and there seem to be some points that most people I know don't really understand or know for certain.As a result I've been completely confused about them,and I could really do with some expert help on them.

Firstly, in my book it says that all the results of special relativity ultimately owe their existence to the relativity of simultaneity.However, thinking about the famous train platform thought experiment I can't get down to explaining time dilation with it.

Also,in the muon experiment(which everyone must be knowing,so I won't describe it),I see the muon's clock to be running slow,so I see it living longer than it should (in my frame of reference).
But the strange thing is that the muon actually doesn't have a clock (which I can observe) to help me detect its slowly running time!
So how do I know (without the muon actually having any clock on it) that its time is really running slow?

The fact is that anyone--even one who doesn't have any knowledge of special relativity whatsoever sees this pheomeon occur and can easily see that the muons survive longer than they should,if allowed to.

Please help me out in this.

 

[superkan619]

Muon expt
The clock on muon runs slower when you see it through your F.O.R. This means(and will always mean) that every process of muon that proceeds in time slows down. The decaying of muon is one such process and hence it slows down i.e half life dilates/increases and more such particles are detected.

If you consider a biological cell, time taken to complete the cell cyle increases. If you consider a television, the time taken for a programme increases (say 30 min to 30.2 min).

Note that their clock slows down but you notice it.

 

[sylas]

Also,in the muon experiment(which everyone must be knowing,so I won't describe it),I see the muon's clock to be running slow,so I see it living longer than it should (in my frame of reference).
But the strange thing is that the muon actually doesn't have a clock (which I can observe) to help me detect its slowly running time!
So how do I know (without the muon actually having any clock on it) that its time is really running slow?

You "know" it the same way you "know" anything in science. Science develops and tests models to describe what we observe occurring in the natural world. The specifics of how time passes at different velocities is thoroughly tested by all kinds of different experiments and observations, and as a result we have the equations of relativity to describe what occurs. A clock is anything that measures time. This includes atomic clocks which test relativity by being flown around the world on airliners, or muons that have a certain time linked decay rate.

You can't "know" it as an absolute truth. But in so far as we know anything in science, time passes more slowly at high speed, and muons and everything else we've been able to test behaves as described with this model.

Cheers -- sylas

 

[Urmi Roy]

From what you people said, it seems easy enough, but special relativity itself is so strange and amazing that it takes a while to get used to it.

I was just thinking that perhaps in nature we always see the speed of light as 'c' so the light which is being emitted by the muon can also reach us at a constant rate only; and so it informs us of the muon's journey at that fixed rate.
Since the muon is traveling towards me its light should (by common sense)come toward me at velocity 'c+ v' (v is velocity of muon) but since the light cannot in reality move at this speed, it moves the distance (c+v)*(ideal lifetime of muon which is 2 micro seconds) at its own speed.This obviously takes more than 2 microseconds and so,by the time light does reach us, we find its duration of travel more han 2 micro seconds -----which is time dilation.

This must sound really crazy, but,as I said, it takes a while to get used to these bizarre consequences of relativity.

Another big problem is that with this dispute between what is true and what isn't , it really isn't clear whether one twin in the twin paradox does really grow older than the other-or whether this effect lasts only during the eperiment itself.

Please do send in some help!

 

[sylas]

From what you people said, it seems easy enough, but special relativity itself is so strange and amazing that it takes a while to get used to it.

That's for sure. But stick with it.

I was just thinking that perhaps in nature we always see the speed of light as 'c' so the light which is being emitted by the muon can also reach us at a constant rate only; and so it informs us of the muon's journey at that fixed rate.

The muon experiment has nothing to do with light; it is purely about the time that muons exist. Muons are unstable and they exist for only a very short time. The time is well known, and it is much much longer than it takes for muons to get to the surface of the Earth from where they are formed by cosmic rays in the atmosphere. But because they travel so close to the speed of light, time passes more slowly for them, which they can reach the surface. Measures of number of muons and cosmic rays are -- like every other experiment trying to test this theory -- explained by the change the rate at which time passes with velocity.

Another big problem is that with this dispute between what is true and what isn't , it really isn't clear whether one twin in the twin paradox does really grow older than the other-or whether this effect lasts only during the eperiment itself.

Please do send in some help!

It's a problem for a student to learn; and I appreciate that. It is also counter intuitive, in the sense that it doesn't fit the intuitions we form from our own experience of small velocities. But the theory itself is crystal clear in its own right. You just have to learn it; and that takes time. We can answer questions, but ultimately you will need to do a bit of study yourself and read up more on the theory. When you get to the point of being able to apply the theory for yourself to a given problem, you have a change of it starting to make more sense to you. As far as special relativity goes, this is actually not very difficult, in a technical sense.

Cheers -- sylas

 

[superkan619]

Another big problem is that with this dispute between what is true and what isn't , it really isn't clear whether one twin in the twin paradox does really grow older than the other-or whether this effect lasts only during the eperiment itself.

This paradoxical experiment is not under the regime of special theory of relativity because. When one twin starts her journey from rest she is infact accelerating. Again when she tries to turn to meet her sister again shen changes her velocity changes and she accelerates. SR works only for inertial i.e non-accelerating frames.

It requires general theory of relativity which involves so much complications that mathematical physicists haven't found time to solve this paradox.

But its for sure that another Einstein will change the scene as it appears now.

 

[sylas]

This paradoxical experiment is not under the regime of special theory of relativity because. When one twin starts her journey from rest she is infact accelerating. Again when she tries to turn to meet her sister again shen changes her velocity changes and she accelerates. SR works only for inertial i.e non-accelerating frames.

It requires general theory of relativity which involves so much complications that mathematical physicists haven't found time to solve this paradox.

But its for sure that another Einstein will change the scene as it appears now.

Incorrect, in all respects.

Special relativity handles acceleration just fine, and the twin "paradox" is easily and simply solved using special relativity alone. It was NEVER a "paradox", merely an interesting consequence of special relativity that trips up people thinking in terms of mistaken intuitions only, without actually using the straightforward calculation.

Where you need the general theory is not with acceleration, but with gravity. In fact, the general theory is derived by using an equivalence of gravity with acceleration under special relativity.

Also, general relativity is more complicated to be sure; but it is not so complicated that it takes up any particular amount of extra time once you've put in the time to learn it.

Cheers -- sylas

 

[Urmi Roy]

Thanks for you expert help.

I'll be looking forward to further assistance in the near future.

Sorry if my questions are a bit dumb,since I've only just passed high school and I just did a bit of extra reading on special relativity before getting into engineering college.

 

[superkan619]

Thanks for you expert help.

I'll be looking forward to further assistance in the near future.

Sorry if my questions are a bit dumb,since I've only just passed high school and I just did a bit of extra reading on special relativity before getting into engineering college.

Me too the same thing...

 

[superkan619]

In fact, the general theory is derived by using an equivalence of gravity with acceleration under special relativity.

I wish I could have referenced this statement in my reserach paper.

 

[superkan619]

Also, general relativity is more complicated to be sure; but it is not so complicated that it takes up any particular amount of extra time once you've put in the time to learn it.

Thank you sylas, p'haps you are mathematical buddy well equipped with Tensor calculus. I haven't yet started my course in vector calculus. By "extra time" I don't mean solving some tensorical equations, but thinking out of GR. To remove its absoluteness of S-T, energy anomaly, to completely (and physically) formulate and prove the General Principle of relativity(key to twin paradox).

So far as the twin paradox is concerned, dozens say they have solved it but no one has been able to put away with the unusual consequence that preferential F.O.R do exist.

No inertial frame is naturally more preferred in SR.
No frame of any kind is naturally more preferred.(GenPrinRel)------>here arises the problem.

 

[Naty1]

From what you people said, it seems easy enough, but special relativity itself is so strange and amazing that it takes a while to get used to it.

This idea "strange and amazing" applies to a lot of science...the more you learn the stranger science gets. Keep that in mind! Time, space and energy are not absolutes..they depend on your frame of reference. Even "worse" everything is "uncertain" no matter how perfect our instruments...even the hardest,toughest metal is 99.99999% "empty space"...

And if you get to quantum mechanics things get even crazier, meaning not intuitive, not consistent with our everyday senses.

Richard Feynman once said something close to "Nobody understands quantum mechanics" and may have also authored "shut up and compute" (I think) meaning that we could argue forever about what the math means, but we can all agree on the correct computations...

 

[Dale]

But the strange thing is that the muon actually doesn't have a clock (which I can observe) to help me detect its slowly running time!

It does have an observable clock: its decay time. It is not a terribly accurate clock for a single muon, but take a few million muons and the half-life is well known to high precision.

 

[Janus]

So far as the twin paradox is concerned, dozens say they have solved it but no one has been able to put away with the unusual consequence that preferential F.O.R do exist.

All that is needed to "resolve" the Twin Paradox without the introduction of a preferential F.O.R. is an understanding and application of:

1. Time dilation
2. Length contraction
3. The Relativity of Simultaneity

 

[sylas]

So far as the twin paradox is concerned, dozens say they have solved it but no one has been able to put away with the unusual consequence that preferential F.O.R do exist.

No inertial frame is naturally more preferred in SR.
No frame of any kind is naturally more preferred.(GenPrinRel)------>here arises the problem.

There's no problem, except for the difficulty of any individual as they learn new ideas. The maths and concepts may be counter intuitive at first, but is not complicated or difficult or paradoxical. There is no preferred frame of reference; you can use any inertial frame you like and get precisely the same result for ages of the twins. Only one twin is an inertial frame of reference themselves, of course. The other isn't. You can use special relativity to calculate all the observations and consequences for an accelerated frame as well, but this generally involves picking an inertial frame (any frame will do, none is preferred) to calculate observations and proper time for the twin that is not inertial. Obviously, you don't do it by thinking they are equivalent to an inertial frame, and if you think there is a preferred frame, then you simply don't understand the maths yet.

That can be fixed... as long as you have the elementary common sense to recognize that perhaps you might NEED to learn something about it before making grand pronouncements.

Cheers -- sylas

PS. I am not good with tensors or GR myself. But I do know SR. And in my opinion, the best first step is simply the Lorentz transformation. "Time dilation" and relativity of simultaneity and all the rest are consequences, but you are better to use the Lorentz transformations directly.

PPS. My apologies if I am stating what you already know. Your comments are not entirely clear to me. When you say "no one has been able to" do whatever it is you think they should do, this makes no sense. You can use GR to describe the accelerated frame if you like, but this is overkill for the problem.

 

[superkan619]

"I often say that when you can measure something and express it in numbers, you know something about it. When you cannot measure it, when you cannot express it in numbers, your knowledge is of a meager and unsatisfactory kind. It may be the
beginning of knowledge, but you have scarcely in your thoughts advanced to the stage of science, whatever it may be."--Lord Kelvin
I accept of my faulty remarks about preferential F.O.Rs.

Only one twin is an inertial frame of reference themselves, of course. The other isn't. You can use special relativity to calculate all the observations and consequences for an accelerated frame as well, but this generally involves picking an inertial frame

For two twins, one accelerating without giving the other some acceleration is impossible. The acceleration is not even a small one in magnitude to be approximated.

Incorrect, in all respects.

Thats the clear reason why I supposed it to be out of SR(although GR depends on SR). Frankly, now I myself is imposed upon a question that if there were three twins, so that the third's acceleration cancels the acceleration of the observer twin, then what might happen?

There is truly something that is forcing me (since 2 yrs) to enquire about what may be called the 4th point in Mr. Janus' list.
I realize it (humbly!) that u guys are tougher than me, really. I've just finished my high school where even S relativity hasn't been taught to us. So, my experiences with SR and GR are more physical than mathematical. Thankx to PF, I am going to refer a more detailed book on it. Please accept me as a kid enquiring about what he loves. I just wanted to expose some of my thinkings(may be childish) to you guys. The concept of cartesian space(PS Don't confuse it with any geometry i.e Euclidean or Reimmanian; also not with an empty set of axes) is one such thing which some of you might be thinking of as a grand pronouncement for you. Thats not the spirit of physics. Forgive the superkan.


Do not go where the path may lead, go instead where there is no path and
leave a trail.-----Ralph Waldo Emerson

 

[sylas]

For two twins, one accelerating without giving the other some acceleration is impossible. The acceleration is not even a small one in magnitude to be approximated.

Nonsense.

Thats the clear reason why I supposed it to be out of SR(although GR depends on SR). Frankly, now I myself is imposed upon a question that if there were three twins, so that the third's acceleration cancels the acceleration of the observer twin, then what might happen?

The motions of a twin are not altered simply by the existence or otherwise of other twins.

I realize it (humbly!) that u guys are tougher than me, really. I've just finished my high school where even S relativity hasn't been taught to us.

It's not a matter of being "tougher"; it's just a matter of learning more about it. Don't be put off by my rather terse answers. You can learn about this stuff; and that's what you really need to do. It's well worth the effort; and understanding it better makes it more fun, in my opinion!

Good luck with it -- sylas

 

[superkan619]

Nonsense.

Please be articulate about what you speak! that's a good old Newtonian concept. When one twin starts her rocket/jetpack she pushes the platform/planet where both the twins were initially standing. Further we will like the acceleration to be from 0 to 0.9c, that's not a small one.

The motions of a twin are not altered simply by the existence or otherwise of other twins.

I think its mistake in my explaining (most probably) or your understanding of the twin paradox. Suppose now that the three twins are standing on the same planet. Two of them start their rockets from diametrically opposite places. In such a case the recoils cancel each other and If we don't talk about the third one It reduces to a problem as you stated earlier with one inertial twin.

 

[superkan619]

It's not a matter of being "tougher"; it's just a matter of learning more about it.
Good luck with it -- sylas

The matter of learning more is what I consider to be "tougher". It was a nice time being with you. Fools talk too much b4 doing much. That is what is the problem with me[God save thy superkan]. I appreciate your understanding of SR and the twin paradox. Let's close this discussion!

Good luck to you Bro!

 

[sylas]

Please be articulate about what you speak! that's a good old Newtonian concept. When one twin starts her rocket/jetpack she pushes the platform/planet where both the twins were initially standing. Further we will like the acceleration to be from 0 to 0.9c, that's not a small one.

You can deal with this case, with SR as well... but it adds nothing particularly relevant to what is actually of concern with the twin problem. In the conventional problem, a twin has a space ship, rather than using the other twin as reaction mass.

 

[Urmi Roy]

Please help me out with this situation in special relativity...
Train-platform experiment(there's an article in wikipedia about it in the page 'relativity of simultaneity').

Suppose Sally is in the middle of a train with a source of light. The source emits light pulses,one toward the front of the moving train and the other towards the back.

Sam also has a similar apparatus,but he is standing on the platform.

Sam observes that Sally's clock are running slow and to him the light pulse moving toward the back of the train reaches the back before the other pulse reaches the front(since the front of the train is moving away from the light pulse which is coming towards it).

The train is also length contracted to Sam,because he locates the front and back of the train at different times(it is not possible to simultaneously note the positions of the front and back of a moving train).

Sally interprets Sam's observations by saying that Sam's clocks were not synchronised properly and so he measured a greater amount of time for her to completely pass the platform.Also,she realizes that Sam measured the time she first appeared at the platform and the time she left it at different times so his calculation resulted in a shorter length than it should be(from her reference frame).
Since Sam is moving (when viewed from Sally's reference frame), the platform is length contracted for Sally.Just as Sam sees Sally's clock running slow,Sally also sees Sam's clock running slow.Sally also sees that the pulses of light in Sam's apparatus do not reach simultaneously.
But the problem is that if Sally says that Sam's clocks aren't even synchronised properly,how can she say that his clocks are running slow? Besides, how is it possible for the platform to seem length contracted to Sally?

 

[Urmi Roy]

No answers?

 

[sylas]

Please help me out with this situation in special relativity...
Train-platform experiment(there's an article in wikipedia about it in the page 'relativity of simultaneity').

Suppose Sally is in the middle of a train with a source of light. The source emits light pulses,one toward the front of the moving train and the other towards the back.

Sam also has a similar apparatus,but he is standing on the platform.

Sam observes that Sally's clock are running slow and to him the light pulse moving toward the back of the train reaches the back before the other pulse reaches the front(since the front of the train is moving away from the light pulse which is coming towards it).

The train is also length contracted to Sam,because he locates the front and back of the train at different times(it is not possible to simultaneously note the positions of the front and back of a moving train).

Sally interprets Sam's observations by saying that Sam's clocks were not synchronised properly and so he measured a greater amount of time for her to completely pass the platform.Also,she realizes that Sam measured the time she first appeared at the platform and the time she left it at different times so his calculation resulted in a shorter length than it should be(from her reference frame).
Since Sam is moving (when viewed from Sally's reference frame), the platform is length contracted for Sally.Just as Sam sees Sally's clock running slow,Sally also sees Sam's clock running slow.Sally also sees that the pulses of light in Sam's apparatus do not reach simultaneously.
But the problem is that if Sally says that Sam's clocks aren't even synchronised properly,how can she say that his clocks are running slow? Besides, how is it possible for the platform to seem length contracted to Sally?

All the consequences follow from the Lorentz transformations. I don't understand what problem you have, apart from it just being counter intuitive. The wikipage describes it well. Relativity of simultaneity.

 

[Urmi Roy]

I've found a webpage from VirginiaTech explaining the twin paradox.

Please look through it,if you are interested.

The site's name is http://www.phys.vt.edu/~jhs/faq/twins.html

There's only one point in the explanation which I don't understand.The explanation seems to be the same as the explanation of other paradoxes like the train-tunnel paradox and the pole-barn paradox,so is the twin paradox just analogous to these other paradoxes,only applied to a different situation, or is there something very different that singles it out?

The acceleration of the traveling twin is not considered essential in the text given in the site and it gives us an explanation of the paradox without any acceleration at all right at the end.
However, it keeps on stating that there are three reference frames in this example rather than two.

(I found an analogous explanation of the train-tunnel paradox, which seems the same as that of the one I referred to in the above lines,here it is --

http://in.answers.yahoo.com/questio...U_p0Hh6RHQx.;_ylv=3?qid=20081230070753AAnHw6W

I just wanted to make sure if the explanation of the train-tunnel experiment as given here is analogous to that of the twin paradox as given in the Virgini Tech site,only applied to two different situations.)

 

[sylas]

I just wanted to make sure if the explanation of the train-tunnel experiment as given here is analogous to that of the twin paradox as given in the Virgini Tech site,only applied to two different situations.)

They are different. The train tunnel involves two inertial frames. The traveling twins involves one inertial frame and an accelerated frame. If you have a very short acceleration period to turn the traveling twin around, then the twin problem has effectively three inertial frames:

• Stay at home twin frame
• Outward bound twin frame
• inward bound twin frame

The tunnel "paradox" has inertial frames for the train and for the tunnel.

Cheers -- sylas

 

[Urmi Roy]

They are different. The train tunnel involves two inertial frames. If you have a very short acceleration period to turn the traveling twin around, then the twin problem has effectively three inertial frames.

I understand this basic difference, but at the end of the day,it seems to have no bearing on the situation itself.

Exactly how or at which point does the drastic difference between the two paradoxes come in?

The explanation for the train-tunnel experiment seems to apply for the onward journey and the home-coming journey (in twin paradox) individually,and all we're doing is to repeat the explanation for each of the journeys--so it is the same(as the train-tunnel paradox),only its done twice for the twin paradox and once for the train-tunnel experiment.

 

[sylas]

I understand this basic difference, but at the end of the day,it seems to have no bearing on the situation itself.

Exactly how or at which point does the drastic difference between the two paradoxes come in?

The explanation for the train-tunnel experiment seems to apply for the onward journey and the home-coming journey (in twin paradox) individually,and all we're doing is to repeat the explanation for each of the journeys--so it is the same(as the train-tunnel paradox),only its done twice for the twin paradox and once for the train-tunnel experiment.

It's all solved with the same physics theory, of course; but you asked about three frames of reference rather than two. That's because one paradox requires three; the other doesn't.

One is dealing with relativity of simultaneity; the other is dealing with proper time on different world lines between the same point.

So it's a different problem, but it's still all solved with the same physics.

 

[Urmi Roy]

From what Sylas stated in the last post, there doesn't seem to be any of that tremendous 'dissymmetry' in the twin paradox which ,makes it so very unique.

In other words, the twin paradox is unique in only that it involves a little more lengthy a process than the other paradox.

 

[sylas]

From what Sylas stated in the last post, there doesn't seem to be any of that tremendous 'dissymmetry' in the twin paradox which ,makes it so very unique.

In other words, the twin paradox is unique in only that it involves a little more lengthy a process than the other paradox.

Not how I would put it; as should have been clear in my first post. They really are different problems and different situations, for all that the same physics can be used to solve each problem.

In fact, it may be actively misleading to describe them as similar. In the tunnel problem, the two observers have a symmetrically equivalent experience. In the twins problem, the two observers DON'T have a symmetrical experience. Nearly all the confusion of people with the twins problem arises precisely because they think that the experience of the two twins is symmetrical in much the same way as the tunnel and train are symmetrical.

That's just wrong. The twins are NOT symmetrical, which makes it a different problem.

Cheers -- sylas

 

[JesseM]

How is the train-tunnel thought experiment analogous to the twin paradox? The train-tunnel scenario is an illustration of the relativity of simultaneity (in one frame the event of the front of the train passing the front of the tunnel is simultaneous with the event of the back of the train passing the back of the tunnel, in other frames it isn't), whereas in the twin paradox you just want to know the age of each twin at the moment they reunite at a common location, and there are no disagreements between frames about the answer to this question since simultaneity disagreements only arise for events at different spatial locations.

 

[Klockan3]

The twin paradox is just that both twins see the other to be ageing faster than themselves in both there and back. Then since when the twin is back they are in the same frame they got to have the same experience meaning that this is a paradox unless you consider the acceleration.

 

[sylas]

The twin paradox is just that both twins see the other to be ageing faster than themselves in both there and back. Then since when the twin is back they are in the same frame they got to have the same experience meaning that this is a paradox unless you consider the acceleration.

Awkward description there... what the twins "see" is Doppler shifted. So you don't actually "see" the same thing as given by time dilation. What ACTUALLY happens is that when twins are receding from each other, each one sees the other one aging more slowly, and when approaching each one sees the other one aging more rapidly. The difference is that the twin that turns around actually sees the other for equal durations of observed approach and recession, whereas the stay at home sees the recession phrase for longer than the approach phase.

It's not actually "acceleration" that is important. It is simply the change in frame of reference. Acceleration is how you move into a new frame of reference; but if there was some topological defect in space; a wormhole that simply reverses the direction of a passing spaceship without actually accelerating anything, then you would still get the same consequence. Likewise for a star trek like "teleporter" used to transfer into a passing ship for the return journey. All that matters is that you somehow change to a new inertial reference frame.

Cheers -- sylas

 

[Urmi Roy]

What the twins "see" is Doppler shifted. So you don't actually "see" the same thing as given by time dilation.

Where does the doppler effect come in,now? I really didn't come across anything on the doppler effect while reading about the twin paradox--is there anything major I'm missing?

What ACTUALLY happens is that when twins are receding from each other, each one sees the other one aging more slowly, and when approaching each one sees the other one aging more rapidly. The difference is that the twin that turns around actually sees the other for equal durations of observed approach and recession, whereas the stay at home sees the recession phrase for longer than the approach phase.

Now, this explanation of the twin paradox doesn't resemble the one I got from the Virginia Tech website. As a beginner, you can imagine how confused I must be feeling right now!

 

[matheinste]

Where does the doppler effect come in,now? I really didn't come across anything on the doppler effect while reading about the twin paradox--is there anything major I'm missing?



Now, this explanation of the twin paradox doesn't resemble the one I got from the Virginia Tech website. As a beginner, you can imagine how confused I must be feeling right now!

Yes the Doppler effect can add an element of confusion. But if you want to know what each twin actually sees during the journey then the Doppler effect comes into play. In the case of the twins we do not really need to know what they see but in what their clocks read at the beginning and end of the journey. The Doppler effect as such has no bearing on their final clock readings when they are colocated.

Matheinste.

 

[sylas]

Where does the doppler effect come in,now? I really didn't come across anything on the doppler effect while reading about the twin paradox--is there anything major I'm missing?

It's not anything particularly major. You spoke of what a twin "sees"; rather than what a twin calculates or infers.

What I really picked up on was the mention of "acceleration". Sometimes people think of something special happening during acceleration; but really all that matters is a change of reference frame. It's not really valid to speak of what happens to a remote twin "during" an acceleration of the other, because that implicitly brings up the notion of simultaneity, and that is a common source of errors.

The proper way to calculate the age of any twin is to integrate the proper time along their world line.

Cheers -- sylas