Question for the experts:

[eon_rider]

I'm trying to get my head around something in S/GR.

 

Say we have a very large train that contains a smaller train with station inside it. (imagine a model train inside a full sized train)

 

Next inside that 2nd model train set is an even smaller 3rd model train set.

Inside this 3rd smaller model train set we have yet another 4th model train set, and so on until we have 10,000 trains travelling with in each other. (like Russian nesting dolls (matryoshka))

 

Luckily, the first train (alpha train) is very large and is several hundred parsecs long.

 

Anyway, the journey of the first train begins.

 

The alpha train takes off from the alpha station at the speed of light, or if that's not possible at .99© {ie. slightly slower than the speed of light}

 

The 2nd train within the Alpha train then takes off at the speed of light {or .99©} in the same "forward and straight line" direction from the rear of the alpha train to the front.

 

Then the 3rd train within the 2nd train takes off at the speed of light or {.99©}.

Then the 4th train within the 3rd train takes off at the speed of light or {.99©}.

 

All in the same direction. Straight ahead. All within their own frame of reference. We repeat this pattern 10,000 times.

 

Can this go on for ever?

Do we ever hit a space/time compression limit?

 

Thanks. Hope this makes sense.

If not, please let me know where you'd like me to clarify.

 

Thanks much for any help, and sorry if this question is elementary.

 

Eon.

[Lars nCo]

I'm pretty sure this isn't applicable since due to E=MC² anything with mass can not travel at a speed equal to or in excess of the speed of light.

[Spyman]

[b']Do we ever hit a space/time compression limit?[/b]

I am not an expert, but from my understanding the limits are zero and lightspeed ©.

 

Thus non of the trains will ever reach the speed of light.

[eon_rider]

EDITED: Thanks guys....I hear what you're saying.

 

Thanks for the reply. Very much.

And You are right, nothing can travel equal to the speed of light.

 

So...let's make it .99c

Would that work?

 

Each train travels, within it's own reference frame at .99©

 

Meanwhile "Space/time" is changing. (compressing or whatever)

 

According to my understanding.

 

My question remains, can we layer the reference frames like this for ever?

( ie. have reference frames nested within each other like this ad infinitum?)

 

thanks

[Spyman]

My question remains' date=' can we layer the reference frames like this for ever?

( ie. have reference frames nested within each other like this ad infinitum?)

[/quote']I would think Yes, why not ?

 

But in the frame of the station the innermost train would still have a velocity below c.

 

Einstein Velocity Addition: http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/einvel.html

 

Which leads me to think that the "compression" never exceeds the limit of c.

(In all frames the "compression" would be below this limit.)

[BigMoosie]

I think it will work, each train would think it is travelling exceptionally fast but anybody standing outside that train or in a train above would see it moving very slowly or not moving at all because time will be alot faster.

[eon_rider]

I have a feeling someone will point out that any space/time distortion (compression) has similar limits related to the fact that nothing but light can travel at the speed of light.

 

Not sure. lol.

 

 

EDIT: AHA....while I was writing this post....

SPYMAN said it!

 

You just answered my question. I think your right.

 

thanks and best,

 

eon

 

PS. thanks Lars and BigM too....

[JaKiri]

I have a feeling someone will point out that any space/time distortion (compression) has similar limits related to the fact that nothing but light can travel at the speed of light.

 

Not just light. All the exchange particles travel at the speed of light (well, maybe except gravitons, but that hardly counts).

[Severian]

The problem is that you are not realizing that the velocity of the train is a frame dependent measurement. When you measure the velocity, the answer you get depends on the train you are in.

 

So if I am in train number 345 and I measure the speed of train 346, I will find it is travelling at 0.99c relative to me. If I am on the ground and measure the speed of train 346 I will find it is travelling at 0.9999999c (or whatever the maths gives). Since the addition of the speeds is not linear when you get near c, none of the trains will ever be travelling at c or faster compared to me. So you can go as far as you want with the train embedding, and you will never reach a limit.

[eon_rider]

Not just light. All the exchange particles travel at the speed of light (well, maybe except gravitons, but that hardly counts).

Today 12:06 AM

 

Thanks...more info....the learning just never stops....good stuff....

I'll study on...

 

So if I am in train number 345 and I measure the speed of train 346, I will find it is travelling at 0.99c relative to me. If I am on the ground and measure the speed of train 346 I will find it is travelling at 0.9999999c (or whatever the maths gives). Since the addition of the speeds is not linear when you get near c, none of the trains will ever be travelling at c or faster compared to me. So you can go as far as you want with the train embedding, and you will never reach a limit.

 

Well now I get it ...thanks for explaining...makes sense...

very clear....Cheers and best.

[Severian]

Not just light. All the exchange particles travel at the speed of light (well, maybe except gravitons, but that hardly counts).

 

In fact, only two of them do: the photon and the gluon (and the graviton if you want to count it). The other force carriers, the W+, W- and Z bosons have large masses, so they do not travel at c.

[[Tycho?]]

The trains would all be going slower than c. They would not reach c in any refference frame.

[Tom Mattson]

Each train travels' date=' [b']within it's own reference frame[/b] at .99©

 

Actually by definition each train travels at 0c within its own reference frame.

[Daecon]

I think the inertia inside the trains will be too great for anything inside to go faster than a crawl, even when all the trains are taken into account and their speeds, the cumulative total could never be light speed as the G-force would be too great for any of the internal trains to be able to move forward.

 

It's all about G-force.

[Severian]

I think the inertia inside the trains will be too great for anything inside to go faster than a crawl' date=' even when all the trains are taken into account and their speeds, the cumulative total could never be light speed as the G-force would be too great for any of the internal trains to be able to move forward.

 

It's all about G-force. [/quote']

 

er... no.

 

As long as the trains are not accelerating there is no force felt by a passenger in any of the trains.

[Daecon]

But... what about when they have to accelerate to get to the almost-speed-of-light?

 

Each train will have to START moving, so would the G-force be cumulative according to the speed of the "reference point" - ie: the train it's on?

[eon_rider]

Posted by Tom Mattson:

 

"Actually by definition each train travels at 0c within its own reference frame."

 

Ok. I believe I get that.

Because with in it's own reference frame the train is not moving at all.

It's standing still. Zero Velocity. (Duh, my bad, as that is suppossed to be one of the major points of GR. )

 

Right?

 

One can only say (the train/the object) is going .99© from the observational reference frame of the train it's travelling in. (or the immediately one bigger train. I can't think of the correct wording for it, but you get the idea.)

 

I hope I get the idea too. LOL.

 

best

 

eon.

[Severian]

But... what about when they have to accelerate to get to the almost-speed-of-light?

 

Each train will have to START moving' date=' so would the G-force be cumulative according to the speed of the "reference point" - ie: the train it's on?[/quote']

 

He never specified how long he took to set up the experiment. Even if the acceleration of each train is only the acceleration of a starting snail they will reach near light speed eventually.

[Thomas Kirby]

I am not an expert, but:

 

E=mc^2 has nothing to do with that. It's the Lorentz framework that predicts infinite mass at the speed of light.

 

I'm pretty sure this isn't applicable since due to E=MC^{2[/sup'] anything with mass can not travel at a speed equal to or in excess of the speed of light.}

[robotochan]

In fact, only two of them do: the photon and the gluon (and the graviton if you want to count it). The other force carriers, the W+, W- and Z bosons have large masses, so they do not travel at c.

 

 

Hmm... thats spun me out, i thought photons were electromagnetic waves and hence the definition of the speed of light is their speed.

 

My addition to this thread is that It would be easier not to consider trains as this puts thoughts in our heads that do in no way mimic those of very fast moving things. If we thought of them as photons (or particles) moving relative to each other then it will be easier to understand. I will take it also as them moveing at 300km/s so with 1000 of these particles moveing as you describe the theory suggests that the finall one P1000 will be moving at 300,000km/s © Now, according to all of einsteins relativity work this should be impossible. But as the speed of light is irrelative (is that a word) and no matter how fast im moving it appears the same speed i.e if im movign 10m/s away from a ligth source pointed at me i will mesure its speed as cm/s not c-10 m/s this would give you the fact that if you were on P1000 it would mesure at c, and if you were at p1 p1000 would mesure at c also. I'm no physics proffesor so i couldn't tell you what this means. But i hope its helped to throw some ideas into your head. I think (but dont quote me on this) that as you move faster time slows down etc, so when observing p1000's speed compared to p999's speed from p1 you will not see a difference in speed of c but only a very small amount, however on p1000 as time is the same it will be as if you have travelled further in the same time. Am i right about that? I think that may be the solution to tyour conudrem if i am.

[robotochan]

He never specified how long he took to set up the experiment. Even if the acceleration of each train is only the acceleration of a starting snail they will reach near light speed eventually.

 

which is where the idea for solar sails came from.

[swansont]

Hmm... thats spun me out' date=' i thought photons were electromagnetic waves and hence the definition of the speed of light is their speed.

[/quote']

 

 

The W+, W- and Z bosons are neither photons nor electromagnetic waves.

[wormholeman]

What a thought!! I think It can go as far as it can, as long as there is a conductor in every-one of those trains. As for limit? I dont know if the universe is unending.

[wormholeman]

I just realized something..How can those trains move in succession to one another.

If the alpha train moves first then the 2nd train where to move the next, and so on

once it reaches 10,000 times? Then you say the alpha train would move again (repeat)

So If all those trains are now at the front of each other? How will they move again????

 

I think we have hit rock bottom!! :I

 

Sorry..

[eon_rider]

Unfortunately, the original thought showed a total conceptual misunderstanding on my part.

 

What was brilliant, and I’m thankful, and I hope I don’t forget is how

Lars n Co, Spyman, Big Moosie, Jakiri (pimpin Nixon, and doom song..lol), Severian, Tycho, Tom Mattson, Transdecimel, Tomas Kirby, robotochan, and Swansont ALL graciously helped clear up the

issue as best they could for a lay person (non expert).

 

My question showed a misunderstanding. The replies all helped to correct it and clarify.

 

I’ll never understand S/GR like most of those guys and gals, but their input

did clarify and correct a few key things and I’m grateful.

 

Yea for physics forum.

 

Ok. .... so thanks,

 

Eon.

 

PS. a little discussion to clear up a misconception is great when it works, but unfortunately not always a guarantee. Still when it works it works.