Time slows down when you approach the speed of light?

[Doc Al]

Regardless kev, the point I was making was that your argument doesn't hold any water on purely logical grounds. And if anything it only reinforces my view that the space inside the spaceships (or trains or whatever) cannot be treated any differently from the space outside - regardless of which frame you are referring to.

By focusing on the details of how the rockets contract (despite there being insufficient information given) I think you distract yourself from the point of this thought experiment. The reason why a flimsy string is used is to make the answer to the question "does it break?" unambiguously yes or no--if there's any stress at all, it will break. While the ends of the string (attached to the rockets) are stipulated to be accelerated uniformly according to Earth observers (this is key!), no details are given about exactly how the rockets are being accelerated.

If, by some strange process that I can't imagine, all the pieces of the rocket are also uniformly accelerated with respect to Earth observers, then you're right--the rocket, unless extremely tough, will be torn apart just like the string. Measured from earth, its length will not contract at all. (Of course, that's because it's being stretched apart by whatever forces are accelerating it!) But there's no reason to assume such a strange arrangement.

In my mental picture of this "paradox" the string is miles long while the rockets are tiny. We care about the string breaking, not about what happens to the rockets--who cares how they contract?

I still have to think over DocAl's referal to the usual problem/explanation of simultaneity.
If anything that is more likely to lead to a loigical explanation. - If there is one. ;-)

I think what I pointed out earlier holds the key to understanding the spaceship paradox and length contraction in general.

Whether an accelerating body contracts or not depends on the details of how it is accelerated. Usually we just assume that somehow the rocket accelerates to some final speed and managed to do that without destroying itself. The idealized case is that the rocket pieces accelerate uniformly with respect to a reference frame co-moving with the rocket (actually a continually changing inertial frame). In that case, the rocket is never under any stress at all--it never changes length with respect to that co-moving frame. Of course, earth observers measure the contraction as the rocket speeds up. (To Earth observers, the pieces do not accelerate uniformly--it's the converse of the Bell spaceship scenario.)

 

[Xeinstein]

catia,

Does time really go slower?

Not in this case. The spaceship pilot will feel normal as stated by the first principle. He will observe that the observer is in slow motion. Neither is really, it only seems that way. Add acceleration to the mix though and you can actually travel to other people’s future.

Are you sure time only "seems" to go slower, Not really goes slower?
If that's the case, then can you tell us why the traveling twin is younger than the one stays at home?

 

[woodmeister]

I saw a show on tv where some understanably skeptical scientists synched 2 very accurate clocks and then put 1 on an airplane flying fast while the other clock was not on the plane. The 2 clocks told different time that was exactly as predicted by Es theory.

 

[Magic Man]

That's about right. If you are going fast enough, you can travel a 7 light year distance (as measured from the Earth frame) in about 1 year of your time. Of course, Earth observers would say it takes about 7 years of Earth time.

See, now that is why I can't understand the general scientific acceptance of this area.

If the destination is seven light years away from Earth, i.e. it takes light severn years to reach us from there, the speed of light is constant etc. then we can calculate the physical distance between the Earth and this destination.

If a spaceship is traveling to this destination it still has to travel that same physical distance irrespective of its speed. How can it do anything other? If the distance is the same and the speed of light is constant, then how can the time taken be anything other than seven years...?

 

[DaveC426913]

Yes, that's exactly the basis of my reply to kev.
The spaceships are not rigid - there's way too many gaps (relatively huge empty spaces) between the atoms/nuclei in a real spaceship.

That's bit misleading, since it implies that, if there were fewer or smaller gaps, it could be rigid enough to transmit a signal ftl.

Without getting too picky about the technical deets, there is one theoretical substance where there are almost no gaps - neutronium - and I'll bet dollars to donuts you can't send a signal through a neutron star ftl either.

 

[Doc Al]

See, now that is why I can't understand the general scientific acceptance of this area.

If the destination is seven light years away from Earth, i.e. it takes light severn years to reach us from there, the speed of light is constant etc. then we can calculate the physical distance between the Earth and this destination.

If a spaceship is traveling to this destination it still has to travel that same physical distance irrespective of its speed. How can it do anything other? If the distance is the same and the speed of light is constant, then how can the time taken be anything other than seven years...?

You miss the point that the measured time and distance for the voyage of the spaceship depends on what frame is doing the measuring. In the Earth frame, of course the distance is 7 light years and the travel time is a bit greater than 7 years. But in the spaceship frame, the time and the distance are quite different.

 

[pervect]

See, now that is why I can't understand the general scientific acceptance of this area.

If the destination is seven light years away from Earth, i.e. it takes light severn years to reach us from there, the speed of light is constant etc. then we can calculate the physical distance between the Earth and this destination.

If a spaceship is traveling to this destination it still has to travel that same physical distance irrespective of its speed. How can it do anything other? If the distance is the same and the speed of light is constant, then how can the time taken be anything other than seven years...?

The problem you have is that you are incorrectly assuming that distance is "physical" and therefore the same for all observers.

The point of relativity is that distance depends on the observer. There is a quantity which involves both space and time defined between two events which is independent of the observer doing the measuring, but this quantity is not distance, but rather the Lorentz interval.

Philosophically, this means that distance is not very fundamental (because it depends on who measures it). The Loretnz interval is a more fundamental and physically significant quantity, just because it is independent of the observer.

 

[Magic Man]

Of course distance is physical, the distance between the two points is a physical constant irrespective of who observes the event or what the observers measure the distance to be.

The spaceship has to travel that same distance between the two points that light travels. If it it traveling at light speed or just below then it can only take seven years or a little more as observed from the Earth. What the guy in the spaceship observers may be different but it is still seven years irrespective of what he interprets the time to be - don't go with this time slows as you approach light speed theory I'm afraid. It's just a speed, why should biological processes slow just because you increase the speed at which the body is traveling let along time itself - what is observed is just that, an observation.

 

[lightarrow]

Of course distance is physical, the distance between the two points is a physical constant irrespective of who observes the event or what the observers measure the distance to be.

"Observes" in this case means "measures". Distance is not invariant, unless with "distance" you mean "distance in the ref. frame in which the two points are stationary".

 

[Magic Man]

Distance in the ref. frame - yes, the actual, real distance, which doesn't change.

Forget all these different frames of reference since they produce incorrect 'observed' measurements.

 

[Doc Al]

Distance in the ref. frame - yes, the actual, real distance, which doesn't change.

Forget all these different frames of reference since they produce incorrect 'observed' measurements.

Enough already. You're behind the times by over a century.