Time slows down when you approach the speed of light?

[yuiop]

You wouldn't be able to tell whether the object is spinning or not unless you were on the outside looking in, but then it would be spinning relative to you. If you were on the object you would be rotating with in such a way that you wouldn't be able to tell. Take Earth for an example: you throw a ball "straight" up in the air, it comes "straight" down to you. The main reason we can tell that the Earth is spinning is due to the changes in our relationship with our sun and moon. This is a very simple point, it can become very complex if we let it, but nonetheless it means that all motion including, including rotational motion or spin, is relative to an external object.

If you used a (very long) tape measure you could detect a bulge at the equator (even the sea bulges) due to centripetal force. If you sent sent two directional radio signals East and West you would find that the West going signal would circumnavigate the Earth faster and return first. You could also transport atomic clocks East and West and find the East going clock loses more time than the West going clock. A gyroscope on your desk would precess every 24 hours. You would observe a similar 24 hour precession in a Foucault pendulum. When you weigh an object at sea level on the equator and then weigh it at sea level at the North pole you would expect a difference due to the difference in radius at those points, but you would find there is very little difference due to centripetal force. If a tunnel was drilled through the centre of the Earth from one point on the equator to another, an object dropped into the tunnel would collide with the East side of the tunnel rather than drop straight through. None of these methods require a sun, moon or stars to detect the spin of the Earth.

 

[dbecker215]

You're right that you would be able to figure out whether it was spinning or not but the thing missing in all this is that your spin is still relative. The spin of the object is relative to the coordinate 0 at the axis of the object. So all the measurements that could possibly be done would conclude that the object was spinning relative to the axis, but none would conclude that the object was spinning in relation to the vacuum of space. You still would not be able to conclude that space itself was not spinning.

 

[yuiop]

If your frame of reference is a point, then you won't experience angular momentumm which means there's no way to tell you're rotating (or more to the point, you cannot rotate)..

It's true that a point particle cannot rotate. However, if we define a point as something with a radius of less than or equal to the Planck length then no elementry particle is a point. Protons and classical electrons are about 10^20 Planck lengths and quark is about 10^17 Planck lengths.

If your frame of reference is not a point, then you are talking about a non-zero radius, which means your angular momentum can just as easily be treated as translational movement over short distances.

If by translational movement you mean linear movement then that kind of motion cannot be detected and can only be expressed relative to an observer. AS HallsOfIvy pointed out, acceleration is absolute in the sense that it can be detected without reference to another body. Rotational or angular motion of a macro object is a form of acceleration and is absolute. I brought up the subject of rotation as the original poster asked if there was anything that was not relative.

 

[lightarrow]

If your frame of reference is a point, then you won't experience angular momentumm which means there's no way to tell you're rotating (or more to the point, you cannot rotate).

If your frame of reference is not a point, then you are talking about a non-zero radius, which means your angular momentum can just as easily be treated as translational movement over short distances.

In this way you could say accelerations don't exist at all...

 

[DaveC426913]

It's true that a point particle cannot rotate. However, if we define a point as something with a radius of less than or equal to the Planck length then no elementry particle is a point. Protons and classical electrons are about 10^20 Planck lengths and quark is about 10^17 Planck lengths.

Correct me if I'm wrong but: subatomic particles act as points, have no inner structure nor anything that could be ascribed to them as "rotating" in the classical sense.

In fact there is no way to tell if a electron (or proton) is rotating, even in principle - in the same way that two electrons (or protons) cannot be distinguished from one another.

 

[yuiop]

Correct me if I'm wrong but: subatomic particles act as points, have no inner structure nor anything that could be ascribed to them as "rotating" in the classical sense.

In fact there is no way to tell if a electron (or proton) is rotating, even in principle - in the same way that two electrons (or protons) cannot be distinguished from one another.

I guess your right. At that level quantum physics prevail and ascribing a exact location or orbit to an electron is pretty much impossible. I am talking about rotation at macro scales but at quantum scales classical physics and even general relativity (as far as I know) break down.

 

[DaveC426913]

I guess your right. At that level quantum physics prevail and ascribing a exact location or orbit to an electron is pretty much impossible.

I wasn't even talking about uncertainty or whether it's measurable. I was simply pointing out that the particles themselves do not have anything that is akin to orientation and thus rotation.

In fact, I'm not even sure a single atom does, though I'm open to education on this. I'm not sure that the orbitals of a single atom can be considred to have an orientation and thus a rotation until they hook up with other atoms.

I am talking about rotation at macro scales but at quantum scales classical physics and even general relativity (as far as I know) break down.

Yeah, but as soon as you talk about anything macro, you involve more than one atom, and as soon as that happens, you can assign both rotation and inertial motion to them.

What I'm getting at is that I think the very idea that "rotational motion can be determined without an external reference" is an illusion. I'm not positive though.

 

[yuiop]

I wasn't even talking about uncertainty or whether it's measurable. I was simply pointing out that the particles themselves do not have anything that is akin to orientation and thus rotation.

In fact, I'm not even sure a single atom does, though I'm open to education on this. I'm not sure that the orbitals of a single atom can be considred to have an orientation and thus a rotation until they hook up with other atoms.

Upon reflection, I tend to agree that you cannot detect rotation in a single atom. The nearest I can find is detection of rotation in a molecule of CF4 in a superfluid.

http://www.sciencewatch.com/may-june2002/sw_may-june2002_page7.htm

Yeah, but as soon as you talk about anything macro, you involve more than one atom, and as soon as that happens, you can assign both rotation and inertial motion to them.

What I'm getting at is that I think the very idea that "rotational motion can be determined without an external reference" is an illusion. I'm not positive though.

A lot depends on what you count as an external reference. Would light count as an external reference? In the case of linear motion, light is not very helpful in detecting your motion as light moves at c with respect to any inertial observer. In the case of rotational motion, the motion can be measured with light by basically using the Sagnac effect. So if you were standing on the inside a hollow cylinder that had a vacuum inside (wearing a space suit) you could work out your rotation rate using light, but without being able to reference anything outside the cylinder. You could assume you are rotating with respect to the vacuum, or you could say that the cylinder is stationary and the vacuum is rotating. You would then have to explain the fact you can comfortably stand anywhere on the curved inner face of the stationary cylinder due to an outward gravitational force caused by the rotating vacuum. The anisotropic behavior of light you observe would be accounted for by a helical spacetime. You would note that when you walk in certain direction and at certain speed that the gravity disappears and you can orbit inside the cylinder. You would put this down to your speed speed matching that of the rotating vacuum so that you are now stationary with respect to the vacuum. Either way you would be assigning special properties to the vacuum.

The problem with rotating vacuum idea is that if you got a cigar tube out your pocket and spun it on an axis tangential to the larger cylinder you would need to superimpose another spinning vacuum tangential to the original one to account for the behavior of the cigar tube. Assuming light travels at a constant c in all directions with respect to the vacuum and that both the cylinders are spinning with respect to the stationary vacuum results in a much simpler model.

 

[DaveC426913]

...the motion can be measured with light by basically using the Sagnac effect.

?

I guess I'll have to look that up.

 

[ΔxΔp≥ћ/2]

catia,

Here is the most intuitive way I have found to understand why one says that time slows down in special relativity.

Special relativity has two very simple, very intuitive postulates and all the consequences of the theory can be understood on a basic level with very simple math.

The first postulate is:
1.The laws of physics are the same in all inertial frames of reference.

This means that if I did an experiment on the earth, for example, and then did the exact same experiment in a car moving at a uniform speed, in a straight line, the results would be the same.

We experience this all the time. If in your car, you decide to throw a ball upwards it will feel exacly the same as if you where at rest. It has been proven experimentally by Michelson, Moreley and others that there is even no way to prove that you are moving if you a going at a constant speed in a straight line.

You may think that you are at rest, but the Earth is now orbiting the sun, that movement we can prove. Ask yourself whether the sun is moving, that we cannot.

2.The speed of light in a vacuum is a universal constant, independent of the motion of the light source.

Imagine that you where to throw a ball at 2m/s. The ball is moving at a speed of 2m/s. Now, if you where to run 2m/s and then throw the ball again, directly in front of you, at the same speed as before, 2m/s, the ball would move at a speed of 2m/s + 2m/s = 4m/s for a stationary observer and 2m/s for you (because you are running towards it). This is how we can move from one reference system to another.

Light is a totally different issue. You can run toward or away from a beam of light and it will not matter. No matter how you are moving with respect to the light, you will measure its speed to be the same.

The two previous postulates seem totally irreconcilable, one is practically the opposite of the other. But do not forget what may be the first physics equation that you ever learned:

Speed = distance traveled / time

It is possible for all observers to agree on the speed of light if their conception of space and time are different.

Since your question was about time, I will show you how it works for time.

Imagine a clock, but this is not your ordinary clock. This clock is quite simple. Take two parallel mirrors and make them face each other, one on the ceiling and one the floor. Now we will place a photon (light particle) so that it may be reflected back and forth between the two mirrors. When it hits the top mirror, we shall hear a "tic" and when it hits the bottom mirror, we shall hear a "toc". We shall now define a unit of time as what must lapse for the photon to travel from one mirror to the other:

Time = distance between the mirrors / the speed of light (constant)

Here is where it gets freaky...

Lets put this clock in a space ship. Let's also make the ship fly by us at a constant speed, in a straight line. The first postulate stated that the pilot of the ship is perfectly valid in stating the he is not moving. Therefore the pilot will experience time flow as defined just above. We however experience something quite different when looking at the pilot:

I shall start with Pythagorean theorem

(Horizontal line)^{}2 +(vertical line)^{}2 = (hypotenuse)^{}2

(I wish I could draw this for you)

Now, using the equation:

Distance = speed x time

We shall replace the horizontal line with a distance (speed of the spaceship x time observer). This is the distance the observer sees the ship travel.

We shall replace the vertical line with a distance (speed of light x time of space ship). This is the distance that the light travels from one mirror to the other viewed from an observer inside the ship. This observer can rightfully say he is at rest.

We also replace the hypotenuse with a distance (speed of light x time of observer). This is the distance that the observer sees the photon make between a tic and a toc.

Simple algebra reveals the proper transformation, but just looking at the triangle, it becomes evident why time cannot be the same.

The same operation can be taken out with the mirrors on the walls parallel to the movement and it becomes evident why people also perceive distances to be different.

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.

I know this was not very visual, but it is the best I can do here.

 

[||spoon||]

About length contraction and time dilation...?

I was thinking the other day, say you were able to travel somewhere at 99% of the speed of light then the factor of length/time dilation would be something like 7. (cant actually remember this may be incorrect but please ignore its not really important!).

So say you wished to travel to a distant planet which from the reference point of someone on Earth was 7 lightyears away. Once you actually got up to 99% of the speed of light the length has "contracted" to 1 lightyear away.

While thinking about this i was wondering "has the length really contracted?? Wasn't the length from Earth to this distant planet ALWAYS 1 lightyear away in the frame of refrence of moving at 99% the speed of light?"

Similarly could you not argue the point that time has not actually dilated, it would always take you 1 year (approximately) to travel to that planet... in that refrence frame.

Im not sure if that makes sense or its just stupid haha, i only just finished high school physics and we didnt do relativity :( If it does make sense is it right or completely off the mark?

 

[dbecker215]

So say you wished to travel to a distant planet which from the reference point of someone on Earth was 7 lightyears away. Once you actually got up to 99% of the speed of light the length has "contracted" to 1 lightyear away.

I don't believe what you're saying is correct simply because if it is 7 light years away then 7 years is the quickest you can get there. For something to be 7 light years away that means that if you were traveling at the speed of light it will take you 7 years to get there. If you are traveling at 99% the speed of light then it will actually take you longer than 7 years to get there because you're traveling slower than the speed of light.

I'm not sure what you're looking for exactly based on this question... sorry.

 

[ΔxΔp≥ћ/2]

Nope, you would get there faster. In your conception of time, time would pass normally. However, because you will see everything else contract, the distance will not be the same.

Light experiences no time.

All this being said though, things would get a lot more complicated than that though, because acceleration would have to be involved.

If I am wrong please correct me.

 

[mihais18]

hello. i have just posted a new thread on time dilation but i would also like to discuss this aspect with you... sorry if i repeat what i have just posted:

I have read a lot of information about time dilation, the twin paradox, the doppler effect and the lorentz transform, but, because I am not a physicist (as a matter of fact i teach french), I have to confess that I understand time dilation only partially.

On the internet there are lots of examples that go with the theoretical explanations. (eg. http://www.phys.unsw.edu.au/einsteinlight/jw/module4_time_dilation.htm or http://www.walter-fendt.de/ph11e/timedilation.htm ). There is this example of the 2 clocks that are synchronized. One of them stays on the earth, the other is placed on a spaceship that travels at near-lightspeed. Both of them work with a light beam that bounces off a mirror. The basic idea is that the clock on the spaceship ticks slower, because it takes the lightbeam more time to bounce off the mirror. There is also the case of the twin paradox that is brought into the discussion.

Now you’ll have to excuse my childish ignorarace: for me these examples only demonstrate that at relativistic speeds a light beam clock ticks slower, not that time itself goes slower. As for the twin paradox, why does the twin brother who travels on the spaceship age slower than the one on earth? In what way are the biological processes slowed down? Is that because the particles of the atoms that make up the human body are also slowed down, just like the light beam?

it is known that for an object that travels at a certain speed time goes slower than for an object that stays still. So I would like someone to explain to me the relationship between speed and time dilation. If this has also to do with light or the speed of light, then I would like to get an explanation about the relation between time dilation and speed of light…

thank you in advance!

 

[||spoon||]

I don't believe what you're saying is correct simply because if it is 7 light years away then 7 years is the quickest you can get there. For something to be 7 light years away that means that if you were traveling at the speed of light it will take you 7 years to get there. If you are traveling at 99% the speed of light then it will actually take you longer than 7 years to get there because you're traveling slower than the speed of light.

I'm not sure what you're looking for exactly based on this question... sorry.

i was under the impression that there was a general agreeance throughout the scientific community that time and length changes according to SR... It seems to me you are neglecting this and are thinking only form a reference frame on earth

 

[yuiop]

.
.
Is that because the particles of the atoms that make up the human body are also slowed down, just like the light beam?
QUOTE]


Basically...yes.

If all biological, physical and chemical processes did not slow down in exactly the same way that a light clock does, then relativity and most of modern physics would be completely wrong. The only thing that does not slow down in an inertial frame is light itself.

But time is relative. Imagine you are a twin that likes reading a lot. You decide your ambition is to read all the books in large library. You work out if you spend every waking hour reading it will take 2000 years to read them all. You jump on a very fast spaceship (which has all the books stored on a computer.) and set about trying to read them all.2000 years later (Earthtime) you return to discover your twin died hundreds of years ago and not only did you not read all the books but that you read no more books than your twin did.

 

[ΔxΔp≥ћ/2]

mihais18,

I would like to refer you to post #40 that I wrote, I know that it is a long read.

Please note that because the observer in the spaceship is valid in stating that he is at rest, he observes the light to travel like someone with the same clock that is at "rest" (on the ground).

The person who observes the spaceship fly by notes that the light travels a longer distance than the one observed by the pilot in the space ship.

If both these people agree on the speed of light, they must disagree on distances and time.

Once you let it sink in that they are both perfectly valid in their statements, it will become obvious why time seems to slow down.

Also note that when the spaceship pilot looks out his window, he will see the observer in slow motion. This is symmetry between the two observers. Both are right.

If you go beyond special relativity and look at general relativity, you will see that you actually can travel to someone’s past or future. (Not really my area of expertise though.

If you have difficulty understanding this in English, I can also explain this to you in French.

 

[yuiop]

?

I guess I'll have to look that up.

This is an informal description of the sagnac effect:

Imagine you have a ring of mirrors so that light can be sent in either direction around the ring and return to its starting point. Imagine that light moves at a constant speed relative to the vacuum. Now if the ring rotates clockwise relative to the vacuum, a light pulse going clockwise around the ring will take slightly longer to return to the start than a pulse going anticlockwise. An interferometer can detect very small differences in the pulse arrival time and is sensitive enough to detect rotations of less than 1 rpm without refence to any external source. (The light source and interfermoter are mounted on the ring.) Real solid state (no moving parts) Sagnac gyroscopes are commercially available and work on this principle. In fact they are replacing traditional high precision, "flywheel" type inertial gyroscopes that are very expensive to make.

 

[dbecker215]

i was under the impression that there was a general agreeance throughout the scientific community that time and length changes according to SR... It seems to me you are neglecting this and are thinking only form a reference frame on earth

It's a bit more complicated than that. Distance, or length, doesn't change with relativity. Distance itself is defined as being a scalar quantity. Scalar quantities do not require direction therefore do not change in a coordinate system. (see Wikipedia for distance, scalar, and magnitude) This means that it is space that warps, b/c space and time are viewed as being inseparable therefore if time warps space must also warp. When you add in space distortion this changes your displacement and your vector, but not distance.

If you can picture some astrological being with a cosmic ruler measuring your scenario of a planet 7 light yrs away, from his perspective the distance you traveled did not change with your speed. Your vector probably will have b/c of the space distortion, but the measuable distance, from point A to point B, did not.

As far as agreeance goes I wouldn't say that loosely. I have read several books on the subject of relativity and time dilation, ranging from textbooks to personal writings from well known physicists, and I wouldn't call it agreeance. There seems to be many disagreements still. Some of this comes from the fact that what experiments we have tend to not line up with the same formula for calculating time dilation. I just read an article the other day about a physicist saying that Einstein's original formulas don't explain the results of different time dilation experiments. I'll have to find his article again and post a thread to get some response. Regardless I am wary of saying that the science community is in agreement.

 

[Doc Al]

I was thinking the other day, say you were able to travel somewhere at 99% of the speed of light then the factor of length/time dilation would be something like 7.

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.

I don't believe what you're saying is correct simply because if it is 7 light years away then 7 years is the quickest you can get there. For something to be 7 light years away that means that if you were traveling at the speed of light it will take you 7 years to get there. If you are traveling at 99% the speed of light then it will actually take you longer than 7 years to get there because you're traveling slower than the speed of light.

You are missing the point. As measured by the space traveler, the distance has contracted to about 1 light year so the time required would only be about 1 year of spaceship time.

It's a bit more complicated than that. Distance, or length, doesn't change with relativity. Distance itself is defined as being a scalar quantity. Scalar quantities do not require direction therefore do not change in a coordinate system. (see Wikipedia for distance, scalar, and magnitude) This means that it is space that warps, b/c space and time are viewed as being inseparable therefore if time warps space must also warp. When you add in space distortion this changes your displacement and your vector, but not distance.

Huh? This is incorrect. Distance is not invariant--it depends on who's doing the measuring.

As far as agreeance goes I wouldn't say that loosely. I have read several books on the subject of relativity and time dilation, ranging from textbooks to personal writings from well known physicists, and I wouldn't call it agreeance. There seems to be many disagreements still. Some of this comes from the fact that what experiments we have tend to not line up with the same formula for calculating time dilation. I just read an article the other day about a physicist saying that Einstein's original formulas don't explain the results of different time dilation experiments. I'll have to find his article again and post a thread to get some response. Regardless I am wary of saying that the science community is in agreement.

Nonsense. There is widespread agreement--and experimental evidence--that special relativity is correct.

 

[||spoon||]

Doc al: is the way i was thinking about the dilation factors wrong?

As in how i think about it is that the distance was ALWAYS 1 light year, but only in the reference frame of 99% the speed of light... and the time taken was ALWAYS 1 year aswell...

So i guess i think of it that time and distance only contract with refernce to some inertial refernce frame... does this make sense?

also if this is true arent there numerous "versions" of the universe, all with different lengths and times dependant on your speed? (im not saying parallel universes but that if we were all moving at 99% of c then everything would seem 7 times closer and this would be the norm)

Thanks

 

[Doc Al]

Doc al: is the way i was thinking about the dilation factors wrong?

As in how i think about it is that the distance was ALWAYS 1 light year, but only in the reference frame of 99% the speed of light... and the time taken was ALWAYS 1 year aswell...

Since distance is always defined with respect to some observer's frame, as long as that frame existed the distance measured by them was the same shorter length (compared to that other frame).

So i guess i think of it that time and distance only contract with refernce to some inertial refernce frame... does this make sense?

Special relativistic effects are always due to the relative motion of reference frames.

also if this is true arent there numerous "versions" of the universe, all with different lengths and times dependant on your speed? (im not saying parallel universes but that if we were all moving at 99% of c then everything would seem 7 times closer and this would be the norm)

I would say there's only one universe, but that the distances and times between various events within that universe depend on who (what frame) is doing the measuring. Since these measurements are frame-dependent, they are less fundamental than we had first thought. To use a weak analogy, just like speed is frame dependent so are distance and time measurements. (But there are quantities which are invariant--the same for all observers; these can be said to represent the more fundamental structure of the universe.)

 

[yuiop]

It's a bit more complicated than that. Distance, or length, doesn't change with relativity. Distance itself is defined as being a scalar quantity. Scalar quantities do not require direction therefore do not change in a coordinate system. (see Wikipedia for distance, scalar, and magnitude) This means that it is space that warps, b/c space and time are viewed as being inseparable therefore if time warps space must also warp. When you add in space distortion this changes your displacement and your vector, but not distance.

The poster was talking about distances as measured by observers in different reference frames, and Doc Al is right in saying they are not invarient. In the example a person at rest with the Earth would say the distance to the planet if 7 light years and the rocket traveler would measure the distance as 1 light year. Neither can prove the other is wrong, as neither can prove they are at rest with some absolute reference frame.

Whether distances are classed as scalar or vector quantities is not really relevant in this context but for the record the distance referred to by x in the Lorentz transformation t = y(t' +vx') and x = y(x' +vt') is a vector quantiy as it can take a + or - sign according to which direction from the origin of the reference frame that the distance x is measured. Perhaps you meant that proper distances (distances that are measured by an observer at rest with the endpoints of the distance being measured) are invarient?

Bell's spaceship paradox provides a good insight into the nature of length contraction and distances in special relativity. I think Bell once said that if you do not understand that the string between the rockets will snap then you do not really undersand relativity. Interestingly, in a straw poll of scientists at CERN theory division, most of the scientists got the paradox wrong!

http://en.wikipedia.org/wiki/Bell's_spaceship_paradox

 

[YellowTaxi]

Bell's spaceship paradox provides a good insight into the nature of length contraction and distances in special relativity. I think Bell once said that if you do not understand that the string between the rockets will snap then you do not really undersand relativity. Interestingly, in a straw poll of scientists at CERN theory division, most of the scientists got the paradox wrong!

http://en.wikipedia.org/wiki/Bell's_spaceship_paradox[/QUOTE]

well if you think the string breaks then you must believe the 2 spaceships actually physically stretch (viewed from their own frame) for precisely the same reason...
So does this actual physical stretching precisley cancel out the observed length contraction seen from the launch-pad ?

 

[phyti]

Here is a simple analogy. I fly from home to a city 200 miles distant at 100 mph in 2 hr.
Later I fly from home to the same city at 200 mph in 1 hr. The distance didn't change, the time did. The space travelers time changes with his speed, he gets there quicker according to his clock. That's because his clock is parsing time into longer units.
Reasoning if his units are longer, there will be more events recorded in them, so he will observe events happening at a faster rate outside his ship in the direction of motion and slower in the opposite direction. Consider the doppler shift, faster ahead, slower behind.
Reasoning tells you launching into space does not shrink the universe! What physical process would accomplish this?

 

[yuiop]

well if you think the string breaks then you must believe the 2 spaceships actually physically stretch (viewed from their own frame) for precisely the same reason...
So does this actual physical stretching precisley cancel out the observed length contraction seen from the launch-pad ?

In the paradox the 2 spaceships accelerate at the same rate. From the launch frame the distance between the 2 spaceships remains the same, but the spaceships themselves appear to be length contracting. If the distance between the spaceships is large compared to the lengths of the spaceships we can ignore the length contraction of the spaceships themselves as far as the string is concerned. Imagine the string is connected from the centre of one ship to the centre of the other, so that the string is unaffected by any change in length of the ships themselves.

From the point of view of the observers on the spaceships the lengths of their ships remains unchanged, but the distance between the 2 ships is increasing. (They can measure that distance by sending light signals from one ship to the other and measuring the round trips times of the signals.) From their point of view, the increasing distance causes the string to stretch and eventually snap. From the launch frame the distance between the two ships remains the same but the string is trying to length contract and snaps because it is shorter than the separation distance.

 

[YellowTaxi]

From the launch frame the distance between the two ships remains the same but the string is trying to length contract and snaps because it is shorter than the separation distance.

Then kev, you're saying that the distance from the front tip to the rear end of each ship will actually increase for the same reason. The ships will eventually tear themselves apart by that logic. On top of that there should be no observable length contraction from the ground.

 

[yuiop]

Then kev, you're saying that the distance from the front tip to the rear end of each ship will actually increase for the same reason. The ships will eventually tear themselves apart by that logic. On top of that there should be no observable length contraction from the ground.

Nope, I said from the launch frame the ships would length contract (tip to rear length). The ships are solid objects made of atoms bound together so they length contract. The distance between the two ships is empty space so it does not pull the ships together. The only thing between the ships is the string, and for the purpose of the paradox it is assumed the string is not strong enough to pull the ships together and snaps.

If the string was replaced by a very strong cable then the ships would be pulled together and the distance between the ships would appear constant to the observers onboard the ships and length contracted to the observers in the launch frame.

Hope that makes sense :P

 

[YellowTaxi]

Nope, I said from the launch frame the ships would length contract (tip to rear length). The ships are solid objects made of atoms bound together so they length contract. The distance between the two ships is empty space so it does not pull the ships together.

??
So if you fly to a distant planet close to c, the space you travel doesn't look length contracted just because it's empty space? That can't be true.

The separation between the 2 spaceships must look length contracted from the ground. If it doesn't then relativity is flawed.

From the ship's point of view, the distance is constant otherwise they would themselves have to stretch (regardless of their size kev ;-) )

ps I understood your argument, it's just a badly flawed one as far as I can tell.

 

[yuiop]

??
So if you fly to a distant planet close to c, the space you travel doesn't look length contracted just because it's empty space? That can't be true.

The separation between the 2 spaceships must look length contracted from the ground. If it doesn't then relativity is flawed.

From the ship's point of view, the distance is constant otherwise they would themselves have to stretch (regardless of their size kev ;-) )

ps I understood your argument, it's just a badly flawed one as far as I can tell.

As you accelerate towards the distant planet, you could imagine that your rocket engines are holding you stationary against a gravitational field that is pulling the planet and the Earth towards some huge black hole behind you. The planet would appear to be accelerating faster towards you than the Earth is receding from you so the distance between the Earth and the planet would appear to be contracting. This is a different situation from the rockets in Bell's paradox because they are both accelerating at the same rate with respect to an observer on the Earth. If the 2 ships accelerated at different rates with the rear ship accelerating faster (so that the gap between them remained constant from their point of view), then the distance between them would be length contracting from the Earth point of view. One way they could maintain constant separation would be to maintain constant tension on the string and then of course the string would not break.


The ships themselves are also length contracting from the POV of the Earth observer, but time dilation of the spaceship clocks and the way they syncronise their clocks make it seem to them that the length of their spaceships remain unchanged.