At speeds close to c, how do lengths change in different reference frames?

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flr

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At speeds close to c, how do lengths change in different reference frames?
« on: 20/04/2012 22:21:34 »
Alice and Bob are here on Earth, and Bob goes to Andromeda at a speed such that the Bob's velocity relative to Alice is  0.999949998 c. The length contraction factor as this speed is: L/L0 = 0.01.

Alice will measure that the distance from her to Andromeda is 2.5 millions ly, i.e. Alice will not see any length contraction from a proper frame. However, Alice will measure that Bob only needs to travel 0.01*2.5 ly to get to Andromeda.

The question is: What Bob sees from a proper frame?
Is he measuring the distance between him and Andromeda as 2.5 millions ly, or only 0.01*2.5ly?

In other words, what is length contracted: Bob in its own proper frame or how Allice from her proper frame sees Bob?

« Last Edit: 21/04/2012 08:27:58 by chris »

MikeS

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Re: At speeds close to c, how do lengths change in different reference frames?
« Reply #1 on: 22/04/2012 07:17:51 »

I haven't given this much thought but wouldn't Bob measure the distance to Andromeda to be the same (at the start of the journey) because as length contracts, so time dilates and the distance remains the same.  (To keep c constant.)

Bob in his local reference frame would not notice length contraction or time dilation.  Alice being a distant observer would.
« Last Edit: 22/04/2012 07:22:36 by MikeS »

yor_on

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Re: At speeds close to c, how do lengths change in different reference frames?
« Reply #2 on: 22/04/2012 18:49:23 »
As soon as you accelerate there will be a Lorentz/FitzGerald contraction. All uniform motions should present us with it too. Otherwise you would have to infer that the only time a 'real' contraction exist is in the acceleration. As all uniform motion are without 'expending energy' locally, but we on the other hand assume a length contraction from eh, Bobs point of view, right as he is the one moving, assumingily uniformly at the time of the question? How does relative motion 'know' its 'speed', as expressed relative that 'inertial observer' I assume Alice to be

Bob does not expend any energy, neither will his and the ships inertia be any bigger as I understands it. What is the gold standard of the universe here?
==

The universe should contract from his frame of reference, although I'm unsure how you think here "Alice will measure that the distance from her to Andromeda is 2.5 millions ly, i.e. Alice will not see any length contraction from a proper frame.

However, Alice will measure that Bob only needs to travel 0.01*2.5 ly to get to Andromeda."

Alice will notice his ship being contracted, ( as well as it should present itself slightly 'rotated' from her frame of reference if I'm thinking right here , as well as Bob 'slowing down' in all manners definable, including red shifting all light signals from him. Her perception of the rest of the universe, as her measured distance to Andromeda, assuming her to have a inertial frame of reference here, shouldn't differ though? Assuming she knows relativity she can calculate it though, what Bob will find from his frame of reference I mean? If that was what you meant?
« Last Edit: 22/04/2012 19:15:49 by yor_on »
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yor_on

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Re: At speeds close to c, how do lengths change in different reference frames?
« Reply #3 on: 22/04/2012 19:25:17 »
Simply expressed. To define different 'uniform motions' you will need some standard, as nothing hinders me from assuming some of them to be infinitely close to lights speed in a vacuum.

Doing so there should be a length contraction of the universe in the direction of that relative motion near lights, from the frame of reference 'relatively moving'. And that length contraction is as far as I'm concerned 'real'  from that point of view. So how do the universe differ between different 'uniform motions' as both inertia, local gravity, mass won't change. But the universe will.
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yor_on

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Re: At speeds close to c, how do lengths change in different reference frames?
« Reply #4 on: 22/04/2012 19:26:42 »
I do have one answer to it
But I'm interested in all views..
==

And this one bears some consideration too

If a length contraction is true, why won't all mass gravitate towards you, as you come infinitely close to lights speed in a vacuum (uniformly moving). You will find a lot of mass, very close to you.
« Last Edit: 22/04/2012 19:33:25 by yor_on »
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flr

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Re: At speeds close to c, how do lengths change in different reference frames?
« Reply #5 on: 23/04/2012 04:16:29 »
OK, I think I finally understood how things are. So Bob moves to Andromeda, constant velocity, inertial SR, Alice stay on Earth.

Alice see Bob length contracted (and time dilated).
Bob will see Alice moving away from him, and Andromeda moving toward to him, at large speeds.
Bob will see Andromeda and Alice length contracted (and time dilated)
For Bob, his ship is of normal size (i.e. not length contracted), it is the Andromeda and Alice who are length contracted.

-----

So, perhaps I could say that Bob is not himself length contracted, but rather Alice see him length contracted, form her own frame of reference.

Similar with Alice, she is not actually length contracted, it is Bob  who see her (from his own frame) as contracted.

-----

Then am I correct to say that:
i) "1 meter ruler in Bob's proper frame is of the same size as 1 meter ruler in Alice's proper frame"
ii) "1 meter ruler in in Alice's proper frame is seen from Bob's proper frame as shorter due to Length contraction"

----------

flr

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Re: At speeds close to c, how do lengths change in different reference frames?
« Reply #6 on: 23/04/2012 04:50:11 »
My feeling is that the length contraction is "apparent" rather than "real". By "real" I mean something is physically compressing along the direction of motion.
Both Bob and Alice see 1 meter ruler be 1 meter in their own proper frame, as if there is no "real" contraction.
The effect of contraction arise when Alice want to compare from her proper frame her 1meter ruler with Bob's 1m ruler; she will see Bob's ruler shorter. If the 'moves' in the Bob's proper frame , their rulers will be as identical and exactly 1 meter.

Having a size of 1 meter in own frame is the same thing as having  0.01 meters from Alice's frame.

Quote
If a length contraction is true, why won't all mass gravitate towards you

Because the length contraction is apparent.

----------------

Why do I have the feeling that time dilation is easier to accept and understand than the length contraction ?

----------------

But in order to make the speed of light c, invariant on observer, we have to accept that time is relative to the observer (easy to be figured out from the "light clock" example") but we also have to accept that lengths are relative to the observer.

What else can be conceived to make c be invariant?

flr

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Re: At speeds close to c, how do lengths change in different reference frames?
« Reply #7 on: 23/04/2012 04:59:07 »

.... wouldn't Bob measure the distance to Andromeda to be the same (at the start of the journey) because as length contracts, so time dilates and the distance remains the same.  (To keep c constant.)

I think at the start of the journey (but when he reached the maximum speed - relative to Alice), Bob will see Andromeda coming toward him at incredible speed, therefore Andromeda is both time dilated and length contracted and she comes on a "distance"/"space" that is length contracted from Bob's proper frame.

Quote
Bob in his local reference frame would not notice length contraction or time dilation.  Alice being a distant observer would.

Alice will see Bob length contracted not because she is a distant observer, but because she have a very high velocity relative to Bob. (or Bob have high speed relative to Alice)

I agree Bob will not see himself length contracted; instead he sees Alice length contracted, but that makes me believe this effect of length contraction is "apparent" and not "real".

flr

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Re: At speeds close to c, how do lengths change in different reference frames?
« Reply #8 on: 23/04/2012 05:28:58 »
If a length contraction is true, why won't all mass gravitate towards you, as you come infinitely close to lights speed in a vacuum (uniformly moving). You will find a lot of mass, very close to you.

The gravity force is
$$G = K \frac{mM}{r^2}$$

I guess r should the proper length,and not the Lorentz contracted length, i.e.
$$r=\frac{r_{contracted}}{ \sqrt{ 1-\frac{v^2}{c^2}} }$$

If so, then again, I think the contracted length rcontracted is "apparent" rather than "real"

yor_on

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Re: At speeds close to c, how do lengths change in different reference frames?
« Reply #9 on: 23/04/2012 14:14:47 »
The problem with a length contraction is that it is a inbuilt function of SpaceTime. It must be a 'mirror' to a time dilation or Einsteins theory will have to be wrong, as I think, but I don't think he is. And the most cited reference there is, is the way muon's can reach, as in being detected by us, further down the atmosphere on Earth than what should be possible.

That they can is defined as a result of them finding a different 'distance', due to their velocity, than the one we measure. and I agree, a time dilation seems easier to understand to me too
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yor_on

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Re: At speeds close to c, how do lengths change in different reference frames?
« Reply #10 on: 23/04/2012 14:25:34 »
And yes, Any contraction you find will have to be the result of there being two, or more, 'frames of reference'. There is no way you will be able to define it without having something to 'compare against'. And what you use when comparing is 'local time' and your 'local ruler'.

But to get it to become an illusion you will need to invalidate Einsteins time dilations too. In the MM experiment you will find a length contraction too, if you think of it.
==

We might be able to see a proof if we ever get to watch the event horizon of a spinning black hole. That as some spin very close to lights speed (assumed from what evidence we've found of BH:s) in a vacuum. And if they spin that fast they must show a Lorentz contraction, as described by the radiation coming from the vicinity of the event horizon, possibly?

If you consider a spinning plate (dish) then as it spin it should 'crack' if the Lorentz contraction is a fact, as it will have different speeds in its material as its 'speed' 'wanders out concentrically' to its rim.
« Last Edit: 23/04/2012 14:46:51 by yor_on »
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yor_on

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Re: At speeds close to c, how do lengths change in different reference frames?
« Reply #11 on: 23/04/2012 15:12:04 »
As for if one meter is one meter, as seen from another frame of reference
Is it real, or an illusion?

If it is real.

Then if A defines the length of B:s ruler as 50 cm, how long will that be true for A? As long as he don't join B:s 'frame of reference', right? There is no way you can keep a 'length contraction', when joining up with that 'frame of reference'. Only in a time dilation will you ever be able to see the direct result of different 'frames of reference' and that only as described by the 'twin experiment' where you have both twins at one origin, one travels, and come back to that same origin. I can't see how that would be possible for a Lorentz contraction though

But 'time dilations' exist everywhere, without disturbing us.

I find those good to read.
Good explanations and just enough math.
Start with Why does relativistic length contraction (Lorentz contraction) happen? and then go to Why does Lorentz contraction only act in the direction of motion? to see how it is thought. And then finally check out the twin experiment.

« Last Edit: 23/04/2012 15:39:00 by yor_on »
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MikeS

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Re: At speeds close to c, how do lengths change in different reference frames?
« Reply #12 on: 24/04/2012 06:07:04 »
Approaching light speed, distance contracts in the direction of travel.  As distance in front of the space-ship contracts, does distance behind dilate?

Geezer

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Re: At speeds close to c, how do lengths change in different reference frames?
« Reply #13 on: 24/04/2012 08:24:18 »

However, Alice will measure that Bob only needs to travel 0.01*2.5 ly to get to Andromeda.

But she can't do that from within her frame of reference. Within her frame of reference, Bob has to travel 2.5 MLY.

A frame of reference does not have a boundary. It includes the entire observable Universe, and you can't be in two different frames at the same time. For Mary to conclude that Bob would only experience 0.025 ly, she would have to be in the same frame as Bob.
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MikeS

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Re: At speeds close to c, how do lengths change in different reference frames?
« Reply #14 on: 24/04/2012 11:16:02 »
Who the **** is Mary?

(With apologies to chubby)

yor_on

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Re: At speeds close to c, how do lengths change in different reference frames?
« Reply #15 on: 24/04/2012 12:21:07 »
Mary will do perfectly for me
As long as she don't laugh at me?

This  'Bob' and 'Alice' drives me nuts, no disrespect meant Flr. It's not your fault that people think it will make it more 'understandable', using real names. I prefer A and B myself, then again, I'm probably slightly senile most of the time.
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Geezer

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Re: At speeds close to c, how do lengths change in different reference frames?
« Reply #16 on: 24/04/2012 17:16:05 »
Who the **** is Mary?

(With apologies to chubby)

She used to hang out with Peter and Paul.
There ain'ta no sanity clause, and there ain'ta no centrifugal force æther.

MikeS

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Re: At speeds close to c, how do lengths change in different reference frames?
« Reply #17 on: 26/04/2012 06:54:22 »
Approaching light speed, distance contracts in the direction of travel.  As distance in front of the space-ship contracts, does distance behind dilate?

Anyone?

yor_on

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Re: At speeds close to c, how do lengths change in different reference frames?
« Reply #18 on: 26/04/2012 11:16:35 »
No, not as I understands it. You're thinking of it in terms of a 'symmetry', right?
And yeah, it's nice thinking Mike, but the symmetry here is the one between a time dilation and its accompanying Lorentz contraction as I think of it.
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MikeS

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Re: At speeds close to c, how do lengths change in different reference frames?
« Reply #19 on: 26/04/2012 15:53:48 »
yor_on

The way I imagine it is with space divided into cubes say with lasers.  As you approach those in front at relativistic velocity they appear to bunch up. Those not in the line of travel remain the same (top, bottom and sides). Those behind I would have expected to dilate.

Also how local is the space contraction effect?  It can't be infinite.

yor_on

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Re: At speeds close to c, how do lengths change in different reference frames?
« Reply #20 on: 26/04/2012 21:42:13 »
Well, as I see it you have to differ between optical effects and the 'room time geometry' getting distorted. Because when you go very fast near lights speed, light will behave differently depending on where it's coming from. http://www.fourmilab.ch/cship/ check out those animations and see.

But yeah the 'boxes' in front will contract from the pilots point of view, but maybe? Assuming very close to light, the universe becomes a perpendicular infinite 'line' of sorts, or more as a 'dish' radiating out? That one is so weird But then you have the way light bends to your motion to consider too. As for what really happens behind your ship though? I think of it as the way we defines photons, some times, which we naturally shouldn't .

That close to light the universe almost must cease to exist, if Einstein is correct.
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