paradox with relativity need help explaining

[somfoolishfoole]

Ok so I'm certain this is not a paradox and I merely need to brush up on my relativity. someone help?

you have object (A) travelling say 95% the speed of light in 1 direction and object (B) travelling in the opposite direction. relativity permits that you select any object as a point of reference, or, a point of "relativity". So my question is this. If you choose the point of view of particle A, and denote 0 velocity to particle A and say that A is not actually moving 95% the speed of light, it is simply stationary and other objects are just moving crazy fast. then isn't object B now traveeling 180% the speed of light away from object A?

I think this next question is probably actually the same issue... but none the less, heres another similare issue.

If you are in a really long space ship which is travelling at 99% the speed of light and you jump on your supercharged motorbike, inside the spaceship and push the turbo button and start travelling on ur motorbike at 99% the speed of light, from the reference point of an outside observer, are you travelling at 198% speed of light?

 

[Architect]

I believe the second example was actually used in Einsteins original paper (I read that years ago but don't recall it in detail).

The answer is no (of course). Taking the second example, that's what the distance and time dilation do, contract space-time so that c_ship == c_outside. So if you run inside a ship going 99% (better example, shoot a bullet at a target at the front of the ship), to an outside observer you, or the bullet, has simply an inertial frame equal to frame of the ship + new contracted frame of the additional velocity. That frame is more contracted than the frame of the ship, thereby guaranteeing c_bullet == c_ship == c_outside.

 

[Ex-User (9086)]

Obj: A,B,O (observer position, where the speeds of A and B were observed, meeting point)
A euclidean vector [Av]O magnitude 95%C direction +, B [Bv]O magnitude 95%C direction -
299 792 458 m / s~c
Unknown: A vel relative to B
VAB=(Av-(-Bv))/(1-(Av*(-Bv))/(c^2))

Spoiler

VAB=0.95c+0.95c/(1-(0.95c*((-0.95c)/c^2))...=
=1.9c/(1-(-0.9025)...=
=0.9986859395532194c

VAB=0.9986859395532194*299 792 458 m/s=299398512.5886991 m/s=>VAB<c

So in case 1 we have a relative speed of over 99% speed of light, addition is only possible when adding small velocities in newtonian system

2nd:
AO,AB=0,99c A relative to 0, B relative to A
find vel. B relative to O(outside observer as in case 1)
we don't know the velocity of a motorbike relative to the observer, so it will be placed as a relation of A to B
-VAB=VA-VB/(1-((VA*VB)/c^2))

Spoiler

-0,99c=0,99c-VB/(1-((0,99c*VBc)/c^2))--c in denominator cancel out, multiply by denominator
-0,99c+0,9801VB=0,99c-VB
1,9801VB=1,98c
VB=0.9999494975001263c

VB=0.9999494975001263 * 299 792 458 m/s = 299777317.7314277 m/s

in case 2 it would be over 99% speed of light too, not 198%

if you seek to understand this you can use something like this

 

[Base groove]

Yah time just slows down to accommodate your twin charged motorcycle.

 

[Ex-User (9086)]

Yah time just slows down to accommodate your twin charged motorcycle.

It depends on what time you mean, motorcycle's time is perfectly fine and it can move at 99%c on his ship. Time runs differently in relation to the observer though.

 

[Hawkeye]

Another interesting fact: At the speed of light, time stops (for the object moving at that speed *if it were possible of course...*) ^^

 

[Goku]

I have a better question: how did The Enterprise accelerate without splattering its crew on the walls? I'm sure it was explained, but I never saw the episode explaining the technology behind that.

 

[Hawkeye]

I have a better question: how did The Enterprise accelerate without splattering its crew on the walls? I'm sure it was explained, but I never saw the episode explaining the technology behind that.

Inertial negation: It's currently an impossible technology based on what we understand about mass.

[edit]

In fact, the only way you could do it is to convert the ship into pure energy.

Faster than Light drives are only necessary if one plans to send data back and forth with a reasonable amount of delay. Apart from that, travelling at lightspeed will get you anywhere instantaneously, be it the moon, or the Triangulum galaxy.

 

[pernoctator]

The term used in the show is "inertial dampers / dampeners". This should only be needed for sub-light speeds though; when inside a warp bubble, the ship itself isn't actually moving.

 

[Ex-User (9086)]

You could have acceleration of 1 light speed /s, to avoid "splattering the crew", you could put this acceleration on every particle that constitutes their bodies, aligning the force vectors so that the distances are maintained. This way you could have a human accelerate to light speed in a second without misplacing his bodyparts or exerting any tidal forces and harming.

Warp bubble is convenient but requires more energy, or so it seems.

 

[Base groove]

OP's paradox is reconciled through realization that time is not absolute. Thus, it is relative to each participant's frame of reference.

Time is actually based on the speed of light, so in this sense, there would be a dispute between the frames of reference as to who was going how fast (and how far and how long it took).

Special relativity predicts the more something approaches the speed of light, the more energy it requires to continue to accelerate, the more massive it becomes, until it becomes infinitely massive and requires an infinite amount of energy to continue accelerating.

 

[Reluctantly]

Basically,

From what I gathered about relativity, it seems Einstein interpreted the results of the Michelson-Morley experiment as meaning that the expansion/contraction of space affected time. He seemed to have related light directly with time and space, in which space and time are considered two aspects of the same thing.

In other words, let say you have three objects, A and B and C, and they are say 1,000 miles apart and form some kind of triangle, like so in space


A <------------1,000 miles---------------> B
^
|
|
|
1,000 miles
|
|
|
|
v
C

Now, as A and B move toward each other at some speed, say 1,000 miles/hour relative to C, the distance between A and B increases some (depending on the speed) relative to C. So what does this mean? It means if A and B move toward each other, then relative to C, C will see that they travel a farther distance than what A and B see they are traveling.

In other words, when A and B measures an hour passing by for them at 1,000 miles/hour and stops, they will think they have traveled 1,000 miles in an hour, relative to C, and be right next to each other. But when C measures the time it took for A to reach B, C sees that they have traveled more than 1,000 miles; so let's say C saw a distance of 1,500 miles and saw them moving 1,000 miles/hour, as we said, relative to C. Then 1.5 hours will have passed for C. Thus time moves slower for A and B, relative to C (only an hour passed for A and B, while 1.5 hours passed for C) OR you could argue that space changed relative to C (the space between A and B expanded while they moved toward each other), rather than time. But either way, they would be the same thing and only understood in a relative manner. So space and time would be dependent. And light then would be measured relatively and would have a theoretical relative maximum because if A and B moved toward each other too quickly, relative to C, there would be infinite space between them and time would stop for them and ... well they would cease to exist, essentially; thus we have a theoretical maximum to the speed of light.

But you could create theoretical scenarios where object A is relative to object B and object B is relative to object C and induct that you could have A moving faster than the speed of light, relative to C. However, measuring light from object A relative to object C is different than measuring light from object A relative to object B relative to object C and A then wouldn't be moving faster than the speed of light, relative to C. Thus the speed of light is a relative concept and the idea of there being a maximum theoretical upper limit applies to analyzing within a particular frame of reference and not frames within frames.

You can read this, if you want something more in depth or you don't understand me - http://galileoandeinstein.physics.virginia.edu/lectures/michelson.html.

 

[Reluctantly]

So to answer your questions,

you have object (A) travelling say 95% the speed of light in 1 direction and object (B) travelling in the opposite direction. relativity permits that you select any object as a point of reference, or, a point of "relativity". So my question is this. If you choose the point of view of particle A, and denote 0 velocity to particle A and say that A is not actually moving 95% the speed of light, it is simply stationary and other objects are just moving crazy fast. then isn't object B now traveeling 180% the speed of light away from object A?

If A moved 95% the speed of light toward another object that was moving say 95% the speed of light toward it as well, then the distance would increase between them and they would each appear to be moving toward each other somewhere in between the speed of light and 95%.

If you are in a really long space ship which is travelling at 99% the speed of light and you jump on your supercharged motorbike, inside the spaceship and push the turbo button and start travelling on ur motorbike at 99% the speed of light, from the reference point of an outside observer, are you travelling at 198% speed of light?

That's a frame of reference within a frame of reference. What would theoretically happen is that the motorbike would also affect the space around it by expanding space in the direction it is traveling toward and contracting the space it is moving away from. In other words, the motorbike, even though in the ship, is theoretically expanding space outside the ship (and not just the ship itself) in the direction it is moving and contracting space outside the ship in the direction is it moving away from. Thus its speed relative to an outside observer would be, again, in between 99% and the speed of light, if it was moving away from that observer.

 

[Ex-User (9086)]

That's a frame of reference within a frame of reference. What would theoretically happen is that the motorbike would also affect the space around it by expanding space in the direction it is traveling toward and contracting the space it is moving away from. In other words, the motorbike, even though in the ship, is theoretically expanding space outside the ship (and not just the ship itself) in the direction it is moving and contracting space outside the ship in the direction is it moving away from. Thus its speed relative to an outside observer would be, again, in between 99% and the speed of light, if it was moving away from that observer.

Wouldn't the speed be the same 99%<x<100%c regardless of whether it is moving away or towards the observer?

What would change though is the contraction or expansion of a visible light from that object.
Correction:If it was moving towards you it (the light reflected) would appear shorter, if it was moving away it would appear longer.

Blueshift/Redshift, doppler + relativity

Imagination helping

The expansion of space as a result of gravity/doppler or universal expansion causes effects that make us conclude that some objects can be moving away from us with a redshift higher than 1.

Highest redshifts are around 8-8.6, this means that the space of origin for the light itself that reached us is so distant, old and that it is moving away at the speed of 8.6 times the speed of light.

Again this object doesn't have this speed, but the place where this object is located changes its distance from ours at this rate.

Limit of lightspeed isn't the speed limit, space can expand at a higher rate.

 

[Reluctantly]

Wouldn't the speed be the same 99%<x<100%c regardless of whether it is moving away or towards the observer?

Yes, I'm sorry. I don't know why I added that in there. The point I think I was trying to make was that space-time would be distorted differently, contracted or expanded, depending on if moving away or towards the observer.

What would change though is the contraction or expansion of a visible light from that object.
Correction:If it was moving towards you it (the light reflected) would appear shorter, if it was moving away it would appear longer.

I'm not sure what you mean by shorter, but the expansion/contraction of space wouldn't exactly be the same thing as a blue and red shift. For example, if an object moves toward another object, because they are moving towards each other, light will compress, even though space is expanded between them. It might be better to think of red shift and blue shift as relating to velocity, while the expansion/contraction of space relates to acceleration; as a force is applied and an object accelerates toward or away from another object, space will expand in the direction of travel and contract behind it, as long as there is acceleration, increasing the expansion/contraction rate with the acceleration.

What's interesting to me is that this implies that as an object moves towards an observer (first accelerating towards the observer before getting to a constant velocity of travel), it will appear bigger to the observer until it decelerates and stops, shrinking to a smaller size during the deceleration. And inversely then, when an object accelerates away, it will shrink instead. This would be the idea behind length contraction.

Blueshift/Redshift, doppler + relativity

Imagination helping

The expansion of space as a result of gravity/doppler or universal expansion causes effects that make us conclude that some objects can be moving away from us with a redshift higher than 1.

Highest redshifts are around 8-8.6, this means that the space of origin for the light itself that reached us is so distant, old and that it is moving away at the speed of 8.6 times the speed of light.

Again this object doesn't have this speed, but the place where this object is located changes its distance from ours at this rate.

Limit of lightspeed isn't the speed limit, space can expand at a higher rate.

Well objects moving away from an observer would have a red shift, increasing as the object got farther away. But that would have nothing to do with the expansion of space. Theoretically, you'd have to measure the rate of change of the change in red shift to determine if the object is accelerating (where a value of zero would mean no acceleration, but a constant velocity), and from that you could deduce that space is contracting and/or expanding, depending on its non-zero value.

But the expansion rate of space wouldn't increase the relative speed of the object. So something moving away from Earth that is measurable by Earth (through light) would have a relative speed to Earth that is less than c, the maximum speed of light.

In other words, from the example I posted above where objects A and B are moving toward each other, say they are moving 90% of the maximum speed of light to each other, then object C would not see them moving at a speed of 180% the maximum speed of light. You could argue that when you account for the expansion in space that they are truly moving 180% the maximum speed of light, but it wouldn't mean much and it disregards the concept of relativity completely, since anything moving faster than the maximum speed of light, relative to an observer, would be completely unnoticeable.

Or think of it another way. Since time on Earth speeds up as time on the object moving away from Earth is accelerating away, then if the object could go relatively faster than the speed of light, the Earth would go through an infinite amount of time, while the object would have no time passed - thus it wouldn't even exist as far as Earth is concerned. It wouldn't make any sense to say objects can travel faster than the maximum speed of light.

 

[Hawkeye]

space will expand in the direction of travel and contract behind it, as long as there is acceleration, increasing the expansion/contraction rate with the acceleration.

It's the other way around; space contracts in the direction of travel. A photon has maximum contraction meaning that point A to point B are pretty much the same point. Light does not experience time, we only perceive its 4D shadow so-to-speak.

 

[Reluctantly]

It's the other way around; space contracts in the direction of travel. A photon has maximum contraction meaning that point A to point B are pretty much the same point.

I'm not sure what you mean, so you'd have to be more specific, but that's not what Einstein got out of the Michelson-Morley experiment. He concluded that the space was expanding for the light that was supposed to be traveling faster, making it travel longer (slowing down time). Or conversely that the light that was supposed to be traveling slower had space compressed, making it travel a shorter distance (speeding up time).
And so maybe I got something mixed up, but it would seem that everything behind the object in motion would compress, whereas everything in the direction of travel would expand; and this understanding does not contradict any of the aspects of relativity.

But if you have a better conceptual understanding that relativity is based upon, where everything about relativity can be derived from it, then please share.

Light does not experience time, we only perceive its 4D shadow so-to-speak.

That's debatable considering that time is used to link space with time. It would be nonsensical to argue that it doesn't relate to time. It's integral to the theory.

 

[Hawkeye]

Here you go:

http://www.youtube.com/watch?v=kGsbBw1I0Rg

 

[Reluctantly]

Well, that doesn't contradict what I said.

From the perspective of the object with slowed time, everything around it that has faster time is compressed. But from the perspective of the object with sped up time, everything around that has slower time is expanded. So if I observe an object accelerating away, it will appear that space in the direction of travel of that object is expanding from my frame of reference, making the object seem smaller to me, thus contraction, while at the same time the expansion creates an opposing equal and opposite compression upon what it's moving away from. It's the same idea behind a car going through a wind tunnel; a suction is created behind the car.

And well, I don't think you understand what I'm saying then. But oh well, I'm going to bed. Good night.

 

[Hawkeye]

Well, that doesn't contradict what I said.

From the perspective of the object with slowed time, everything around it that has faster time is compressed. But from the perspective of the object with sped up time, everything around that has slower time is expanded. So if I observe an object accelerating away, it will appear that space in the direction of travel of that object is expanding from my frame of reference, making the object seem smaller to me, thus contraction, while at the same time the expansion creates an opposing equal and opposite compression upon what it's moving away from. It's the same idea behind a car going through a wind tunnel; a suction is created behind the car.

And well, I don't think you understand what I'm saying then. But oh well, I'm going to bed. Good night.

You appear to be mixing it up with the phenomenon experienced when using a Warp Drive. Again, contraction always occurs in the direction of motion (including warp drive technology)

Warp Drives do not use the speed of light for space-time manipulation, instead they compress space in front of the ship and expand the space behind it.

When you use the speed of light or speeds close to it, there is only length contraction.

This rocket and barn for example:

From the barn's point of view the rocket easily fits in the barn when travelling close to the speed of light.

Space hasn't expanded around the rocket. The rocket has merely been compressed. If the space around it expanded, the dimensions of the barn would visibly change too.



Likewise, from the perspective of the rocket, the barn has been compressed.

 

[Vrecknidj]

http://en.wikipedia.org/wiki/Lorentz_factor

 

[Base groove]

Actually, the missing factor that has not been addressed at all, which is a pivotal component of special relativity, is the equivalence of mass and energy. I did make mention of this earlier bit it got buried in all the time dilation/length contraction talk, which are physical manifestations/logical predictions of the theory rather than the preliminary postulates that govern it.


Some time passes, some reading occurs

Ok, so after reading the article again, apparently mass-energy equivalence is just another prediction of the theory, along with the Lorentz transformations.

 

[Base groove]

When you use the speed of light or speeds close to it, there is only length contraction.

I'm sorry but although your explanation was very sound and informative, you fail to acknowledge that time dilation and length contraction are actually the same phenomena (Lorentz transformations) expressed in different perspectives (frames of reference, if you will).

 

[QuickTwist]

No object can move the speed of light because in the manipulation of matter the atoms will essentially break down.

 

[Hawkeye]

I'm sorry but although your explanation was very sound and informative, you fail to acknowledge that time dilation and length contraction are actually the same phenomena (Lorentz transformations) expressed in different perspectives (frames of reference, if you will).

Time dilation was irrelevant to the context of the discussion. We were talking about the spatial aspect.


Besides, I reference time dilation in my first post.

 

[Base groove]

I reference time dilation in my first post.

Another interesting fact: At the speed of light, time stops (for the object moving at that speed *if it were possible of course...*) ^^

That is interesting!

 

[Ex-User (9086)]

Yes, I'm sorry. I don't know why I added that in there. The point I think I was trying to make was that space-time would be distorted differently, contracted or expanded, depending on if moving away or towards the observer.

Lorentz Transformation

Spoiler

Spoiler

I'm not sure what you mean by shorter, but the expansion/contraction of space wouldn't exactly be the same thing as a blue and red shift. For example, if an object moves toward another object, because they are moving towards each other, light will compress, even though space is expanded between them. It might be better to think of red shift and blue shift as relating to velocity, while the expansion/contraction of space relates to acceleration; as a force is applied and an object accelerates toward or away from another object, space will expand in the direction of travel and contract behind it, as long as there is acceleration, increasing the expansion/contraction rate with the acceleration.

I cannot agree, redshift is used as a confirmation of space expansion over the distance and was used to help set Hubble's Law.
Metric Expansion of Space

Well acceleration is just an increase in speed over short periods of time, usually m/s^2. Light waves emitted by the object moving away will be contracted in the opposite direction and longer in the observer's direction which will give this doppler's effect. Light waves are emitted in this way because the object is contracted or longer to the external observer. So contraction and blueshift are linked.

Spoiler

What's interesting to me is that this implies that as an object moves towards an observer (first accelerating towards the observer before getting to a constant velocity of travel), it will appear bigger to the observer until it decelerates and stops, shrinking to a smaller size during the deceleration. And inversely then, when an object accelerates away, it will shrink instead. This would be the idea behind length contraction.

http://www.youtube.com/watch?v=kGsbBw1I0Rg
Hmm I think it is the opposite, objects that are parallel and on your yourse will appear contracted on the line you are travelling, and distorted but unchanged otherwise in all the other directions.

Spoiler

Well objects moving away from an observer would have a red shift, increasing as the object got farther away. But that would have nothing to do with the expansion of space. Theoretically, you'd have to measure the rate of change of the change in red shift to determine if the object is accelerating (where a value of zero would mean no acceleration, but a constant velocity), and from that you could deduce that space is contracting and/or expanding, depending on its non-zero value.

Well it has to do with expansion of space . Please send me your materials, I sent mine and you can freely read into and confirm stuff. There are no constant velocities in space, theese are possible only in reference frames, the larger the reference frame the less constants and more shifting. Well you deduce it's contraction from the visible light that reaches you that carries the information, so that objects appear shorter/longer, so it doesn't matter if you see the actual acceleration, this object will appear shorter or longer just because it moves relative to you.

Spoiler

But the expansion rate of space wouldn't increase the relative speed of the object. So something moving away from Earth that is measurable by Earth (through light) would have a relative speed to Earth that is less than c, the maximum speed of light.

Yes that was what I was talking about, I did mention that however the increase of distance between two ends of the universe can be multiple times larger than the speed of the light however the speed at which objects are moving away relative to each other is at the speed of almost 100% C, because that is the maximal measured change in space time.

Spoiler

In other words, from the example I posted above where objects A and B are moving toward each other, say they are moving 90% of the maximum speed of light to each other, then object C would not see them moving at a speed of 180% the maximum speed of light. You could argue that when you account for the expansion in space that they are truly moving 180% the maximum speed of light, but it wouldn't mean much and it disregards the concept of relativity completely, since anything moving faster than the maximum speed of light, relative to an observer, would be completely unnoticeable.

It matters in regards of relativity, and objects are not moving towards each other at theese speeds because space expands always from you. So hubble effect and expansion of space happens always from your relative position outwards.
It can only happen with objects that move away from you to have an increase of distance to you more than 100%C but to remain at the non C speed in the reference frame.

Spoiler

Or think of it another way. Since time on Earth speeds up as time on the object moving away from Earth is accelerating away, then if the object could go relatively faster than the speed of light, the Earth would go through an infinite amount of time, while the object would have no time passed - thus it wouldn't even exist as far as Earth is concerned. It wouldn't make any sense to say objects can travel faster than the maximum speed of light.

They do not travel faster than light, they change distance faster than light, it goes from redshift and hubbles law as I have already mentioned

To summarise:
If max speed is C then:
You can move at more than max speed by changin the spacetime itself thus contracting the distance and contracting the coordinates.

All of the coordinates come from a single point and are constantly dividing so it is an illusion of velocity and is just and increase in a scale of entire universe.

If you move at speed C then:
Space is already contracted so that every object you measure relative to you is where you are . Time stops, or to accomodate, time doesn't go forward.

Redshift 8:
You run at the speed of 99.9% light and the floor streches at 8.008+ times the distance you have ran. Quite depressing but it can help visualise.

Lol now that I read this thread Hawkeye did send the same vid .

 

[Reluctantly]

@Blarraun
Right, but I didn't say a blue or red shift couldn't tell you if space is expanding or contracting. It can and it does simply because objects are moving away. However the expansion/contraction due to relativity requires acceleration to warp space. That expansion rate, due to relativity, is what I thought we were talking about. And without acceleration, that expansion rate does not exist.

@Hawkeye
http://www.youtube.com/watch?v=b_PtnzqxEFQ
I don't know, this paints a different picture. And it's strange that I could see it your way and my way and relativity would still make sense. Do you have a concept or proof of why it would have to be the way you say it is then?

 

[Hawkeye]

It's the same thing as taking two derivates of a distance displacement function for an object over time, getting its continuous acceleration, but if there is no acceleration, there is no space contraction/expansion because there is no force. It's a caveat people seem to ignore.

This is incorrect as Special Relativity does not usually deal with acceleration (that is more a General Relativity thing). Length contraction occurs as you increase (not to be confused with accelerate) your speed.

[edit]

I will add more soon but I am fuggered... Plus typing this on a phone is rhubarb...

 

[Reluctantly]

Okay, I edited that post because I realized I'm not being clear.

It's the acceleration that expands the space, due to relativity. Once you are at a velocity and acceleration stops, space is now expanded and what you posted, surely I agree with. The object will be compressed, from an observer looking at it pass by, but it will not continue to get smaller. This is what I meant originally. But please respond (when you get a chance) as to why space must expand behind the moving object and not in front. Everything about relativity still holds true for both scenarios and I find it kind of strange.