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Author Topic: Does Lorentz contraction affect a stationary object that you pass at high speed?  (Read 33297 times)

Offline lightarrow

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If 2 objects are following each other at relativistic speed then the distance between the front and back of each object appears to shrink. So what about the distance between the back of the first object and the front of the second? Does that also appear to shrink so that they seem closer together?

 ???
Of course.
If you travelled at very high speed(*), you would measure all distances between points (which are moving with respect to you) as contracted, independently where those points are (in matter or in the void). At very high speed, not only you would measure all bodies, example planets and stars, as "compressed" in dishes, but also theire distances would be so. In a few seconds (or more or less, according to your speed) you could travel along all the universe.

(*)Of course the same if bodies travelled and you were still, there is no difference, what counts is relative motion.
« Last Edit: 22/03/2009 20:37:13 by lightarrow »
 

Offline DoctorBeaver

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You've touched on what I was wondering. Would that be a way for us to see what is outside our visible universe? If we were travelling at relativistic speed, the distance between us and the visible horizon would be less. Does the contraction mean we could see past it or would time dilation rear its ugly head and prevent it?
 

Offline lightarrow

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You've touched on what I was wondering. Would that be a way for us to see what is outside our visible universe?
Certainly, you would be able to go everywhere in the existing universe, visible or not.
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If we were travelling at relativistic speed, the distance between us and the visible horizon would be less. Does the contraction mean we could see past it or would time dilation rear its ugly head and prevent it?
The lenght contraction means that you could arrive there in a few seconds, and, furthermore, that light from a distant source beyond the limit will have to cover a less distance to reach us, but we couldn't see past it from the beginning, we should wait to meet the light (emitted from the distant source) at ~ half journey.
« Last Edit: 22/03/2009 23:04:22 by lightarrow »
 

Offline DoctorBeaver

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Thank you, Alberto.

Is there a limit to the amount of contraction or is it another 1 of those horrible infinity things? At c, does everything have zero length?

You see, there was another side to this that I was wondering about and that's why I mentioned time dilation. If you could travel at, say, 0.99c, how much contraction would there be between you and the horizon of the visible universe? Or does contraction only apply when you pass someting?

Here's what I was puzzling over. In our frame of reference here on Earth it has taken light 13.7 billion years to get here. Now, nothing can travel faster than c and in your own frame of reference it doesn't matter how fast you go, time will appear to pass at the normal rate. So, it should take you more than 13.7 billion years to get there by your own timescale. But, if the distance is greatly contracted then at 0.99c it may take you less than 13.7 billion years to get there. That can't be right.

The only solution I can see is that time dilation must come into it somehow but I can't figure out how because in your own frame of reference there shouldn't be any. Or is there something else that I'm missing completely?
« Last Edit: 24/03/2009 01:18:16 by DoctorBeaver »
 

Offline lightarrow

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Thank you, Alberto.

Is there a limit to the amount of contraction or is it another 1 of those horrible infinity things? At c, does everything have zero length?
Yes.

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You see, there was another side to this that I was wondering about and that's why I mentioned time dilation. If you could travel at, say, 0.99c, how much contraction would there be between you and the horizon of the visible universe?
Sqrt(1 - 0.992) ~ 0.14, so 1km --> 0.14km.

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Or does contraction only apply when you pass someting?
No, always.

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Here's what I was puzzling over. In our frame of reference here on Earth it has taken light 13.7 billion years to get here. Now, nothing can travel faster than c and in your own frame of reference it doesn't matter how fast you go, time will appear to pass at the normal rate. So, it should take you more than 13.7 billion years to get there by your own timescale.
Haven't understood this one.

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But, if the distance is greatly contracted then at 0.99c it may take you less than 13.7 billion years to get there. That can't be right.
Why? You get there in 13.7*0.14 = 1.92 billion years.

If you want to get there in 1 year (for example), you should travel at:
0,9999999999999999999999733603282c.

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The only solution I can see is that time dilation must come into it somehow but I can't figure out how because in your own frame of reference there shouldn't be any. Or is there something else that I'm missing completely?
Can't grasp your actual concern.

Edit: I made a slight mistake in my previos computation of the time you need to get there; actually is 1.92/0.99 = 1.94 billion years.
« Last Edit: 24/03/2009 20:05:19 by lightarrow »
 

Offline dlorde

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... in your own frame of reference it doesn't matter how fast you go, time will appear to pass at the normal rate.
Consider what this actually means. What would you expect to see if this was not true?

You can look out to other frames of reference and see them running fast or slow by your watch, but time is always going to be uniform in your own frame of reference, so it can only run fast or slow relative to another frame. You will always see your watch running at the same rate, whatever happens, because if time slows or speeds up (relative to an external frame) for your watch, it slows or speeds up for everything else in your reference frame, including your physiology, the operation of your brain, etc.

If that's not what you meant, I'm curious to know what you did mean.
 

Offline DoctorBeaver

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dlorde - That is precisely my point.

Alberto - You said "You get there in 13.7*0.14 = 1.92 billion years.".

From the point of view of someone on Earth, it has taken light 13.7 billion years to make the journey. From the perspective of someone travelling at 0.99c light would still be travelling at c relative to him (basic GR). Therefore, to him light would still take 13.7 billion years to travel that same distance. Am I right so far?

If so, then it follows that he cannot possibly cover the same distance in 1.92 billion years in his own frame of reference. To do so he must travel at 13.7/1.92 = 7.14c. How does that resolve?

 
 

Offline lightarrow

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dlorde - That is precisely my point.

Alberto - You said "You get there in 13.7*0.14 = 1.92 billion years.".

From the point of view of someone on Earth, it has taken light 13.7 billion years to make the journey. From the perspective of someone travelling at 0.99c light would still be travelling at c relative to him (basic GR). Therefore, to him light would still take 13.7 billion years to travel that same distance. Am I right so far?
No, because the distance is smaller. Let's say that at 13.7 billion light years (limit of visible universe) there is a quasar which name is "Q" and that from there a beam of laser light is sent in direction Earth at the moment of your passing close to Earth, in direction Q, with your starship, at 0.99c. Inside your starship you measure as distance from you and Q:  1.92 billion light years. How long will something travelling at c take to reach you? time = space/velocity = 1.92 billion light years/c = 1.92 billion years, so you would receive the beam of laser light in 1.92 billion years.
« Last Edit: 24/03/2009 20:32:18 by lightarrow »
 

Offline DoctorBeaver

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So if you were travelling at 0.99c the light from the edge of the visible universe would take considerably less than 13.7 billion years to reach Earth? The visible edge would no longer be 13.7 billion years * 300,000km/sec distant?

How far does the contraction go? From the photon's perspective, would the distance be zero?
 

Offline lightarrow

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So if you were travelling at 0.99c the light from the edge of the visible universe would take considerably less than 13.7 billion years to reach Earth?
No, to reach *you*.

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The visible edge would no longer be 13.7 billion years * 300,000km/sec distant?
You should have written 13.7 billion years * 1 light year/year = 13.7 billion light years, however it wouldn't be that distance anylonger *for you*;  for Earth would be the same.

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How far does the contraction go? From the photon's perspective, would the distance be zero?
The photon's perspective doesn't exist. Let's talk about the perspective of a passenger travelling at near c: yes.
 

Offline DoctorBeaver

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So if you were travelling at 0.99c the light from the edge of the visible universe would take considerably less than 13.7 billion years to reach Earth?
No, to reach *you*.


But, surely, you would see the distance between the edge and Earth contracted therefore light would travel that distance in less than 13.7 billion years.

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How far does the contraction go? From the photon's perspective, would the distance be zero?
The photon's perspective doesn't exist. Let's talk about the perspective of a passenger travelling at near c: yes.

My brain is going to hurt again now. I just know it.

OK. So at (near)c distance reduces to zero. Therefore it must take zero time to get anywhere as everywhere would be in the same place but of zero length. That sounds like a singularity to me  ???

Would you yourself be contracted to zero size? If not, how could you fit there? And if it is only length that is contracted, does that mean that everything becomes 2-dimensional? I don't like the thought of that.
« Last Edit: 24/03/2009 21:07:55 by DoctorBeaver »
 

Offline lightarrow

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No, to reach *you*.
But, surely, you would see the distance between the edge and Earth contracted therefore light would travel that distance in less than 13.7 billion years.
Yes, but while *in your frame of reference* light will meet Earth in 1.92 b.y., *in the Earth frame* it'll be 13.7 b.y.

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The photon's perspective doesn't exist. Let's talk about the perspective of a passenger travelling at near c: yes.
My brain is going to hurt again now. I just know it.
OK. So at (near)c distance reduces to zero. Therefore it must take zero time to get anywhere as everywhere would be in the same place but of zero length. That sounds like a singularity to me  ???
Infact it's even for this reason that the photon's perspective doesn't exist  :).  If you talk about "near c", instead, then distances and time intervals of travels are not zero, even if as little as you want, approaching c.

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Would you yourself be contracted to zero size?
You wish it was!  ;).  Apart from jokes, from your frame of reference in the starship, everything and of course everyone moving with respect to you would be contracted, not yourself (but you would be contracted *for them*).

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If not, how could you fit there? And if it is only length that is contracted, does that mean that everything becomes 2-dimensional? I don't like the thought of that.
Yes, the "thickness" in the direction of movement would tend to reduce to zero so everything would become bidimensional. You don't like it? But do you realize that you need almost an infinite amount of energy to reach almost c? It's not just to push on the accelerator...
 

Offline DoctorBeaver

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The thought I don't like is that dimensions can be reduced to zero size by velocity. What does that say about our concept of dimensions? Or time, for that matter?
 

Offline yor_on

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In fact that is one of the most confusing truths I know of Lightarrow:)
And a very nice description/discussion btw.

We know that a photon at all times moves at 'c' (depending on density:)
We also know that it has a 'duality' (light 'matter')

Therefore, from the perspective of that photon, on one hand I could say that it both encompass all 'time' there ever has been, as well as say, ah, on the other hand, that it has no 'time' at all as it doesn't really exist in 'time'. Encompass all 'time' as that very first one, if seen as a particle :) would should and will see our universe die, or rather, not even notice it at all from its birth to its death. I love it ::))

On the third hand though :) it's photons that interact with us all, from the ones showing of 'at' our atoms to the ones we can see ((you've already heard that we can see a photon I presume :) Is that a true statement btw?:)

And it's this last remarkable ability that really freaks me 'off' and on...
That they can 'interact' in time I mean, not that we might be able to see one with our eyes.
Anyway you look at it, and I have looked at it :), I still having trouble reconcile myself with its 'ability' to interact in 'time' while in itself more or less, to my eyes that is, existing 'outside' of it.

----

If you like, thinking of that very first photon coming into 'existence' you could ask yourself if there could exist any more photons as seen from the perspective of that first one, where would they take 'place'?
« Last Edit: 25/03/2009 00:13:28 by yor_on »
 

Offline DoctorBeaver

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And it's this last remarkable ability that really freaks me 'off' and on...
That they can 'interact' in time I mean, not that we might be able to see one with our eyes.
Anyway you look at it, and I have looked at it :), I still having trouble reconcile myself with its 'ability' to interact in 'time' while in itself more or less, to my eyes that is, existing 'outside' of it.

Which is something I was getting to. I was taking it 1 step at a time to make sure I was thinking correctly.
 

Offline yor_on

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Ouch DB, sorry, my only defense would be that the questions you state are similar to my own:)
 

Offline lightarrow

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The thought I don't like is that dimensions can be reduced to zero size by velocity. What does that say about our concept of dimensions? Or time, for that matter?
It's only a mathematical limit, you will never be able to reach exactly c, so why do you worry about it exactly?
 

Offline LeeE

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And it's this last remarkable ability that really freaks me 'off' and on...
That they can 'interact' in time I mean, not that we might be able to see one with our eyes.
Anyway you look at it, and I have looked at it :), I still having trouble reconcile myself with its 'ability' to interact in 'time' while in itself more or less, to my eyes that is, existing 'outside' of it.

Which is something I was getting to. I was taking it 1 step at a time to make sure I was thinking correctly.

One possible way of interpreting it is that what we view as the photon's movement through space seems, to the photon, to be it's movement through time; the photon doesn't think it's moving through space at all but believes it's stationary (that's if a photon were to have any awareness, of course).
 

Offline DoctorBeaver

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The thought I don't like is that dimensions can be reduced to zero size by velocity. What does that say about our concept of dimensions? Or time, for that matter?
It's only a mathematical limit, you will never be able to reach exactly c, so why do you worry about it exactly?

OK, forget zero size. Their effective size can be altered by velocity. I find that troublesome.
« Last Edit: 25/03/2009 22:15:51 by DoctorBeaver »
 

Offline lightarrow

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OK, forget zero size. Their effective size can be altered by velocity. I find that troublesome.
Why?
 

Offline DoctorBeaver

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I just don't like the thought of it. It just seems wrong. I want to punch it.
 

Offline lightarrow

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I just don't like the thought of it. It just seems wrong. I want to punch it.
What is "wrong" it to ascribe essential meanings to the concepts of "space" and "time"; they haven't.
(But we were born with them so it's difficult for us humans to get rid of them).
 

Offline DoctorBeaver

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What is "wrong" it to ascribe essential meanings to the concepts of "space" and "time"; they haven't.
(But we were born with them so it's difficult for us humans to get rid of them).

It's not that it's difficult for me to accept that space & time are not rigid structures. I understand warping & contraction of space, and its implications, due to gravity. My problem is getting to grips with the notion that distances can get shorter as we move faster. I know the difference would be immeasurably small, but if I walk somewhere it will be further than if I drive there at 100mph.

I fully accept time dilation and I don't have a problem with that as I more-or-less understand the reasoning behind it. But I don't understand contraction of distance in the same way. Maybe if I did I would feel happier about it.
 

Offline lightarrow

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What is "wrong" it to ascribe essential meanings to the concepts of "space" and "time"; they haven't.
(But we were born with them so it's difficult for us humans to get rid of them).

It's not that it's difficult for me to accept that space & time are not rigid structures. I understand warping & contraction of space, and its implications, due to gravity. My problem is getting to grips with the notion that distances can get shorter as we move faster. I know the difference would be immeasurably small, but if I walk somewhere it will be further than if I drive there at 100mph.

I fully accept time dilation and I don't have a problem with that as I more-or-less understand the reasoning behind it. But I don't understand contraction of distance in the same way. Maybe if I did I would feel happier about it.
As i tried to explain (probably I didn't succeed  :)) it's not a "real" contraction in the sense that there is no internal tension; you could think of it as an "artefact" of how we *define* distance between two points: you have to measure the two points positions *simultaneously*. To do this, the points have to send their position information to the experimenter, and this is done with light, which has not an infinite speed, so these informations don't arrive simultaneously to a moving experimenter, if they arrive simultaneously to an experimenter at rest. For this reason their distance is not the same anylonger. Don't know if you now grasped something.
 

Offline DoctorBeaver

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Alberto - I'm just getting more confused now.

Look at this quote:

The lenght contraction means that you could arrive there in a few seconds, and, furthermore, that light from a distant source beyond the limit will have to cover a less distance to reach us, but we couldn't see past it from the beginning, we should wait to meet the light (emitted from the distant source) at ~ half journey.

Your reply states (where I've highlighted it) that the distance would be less yet now you are saying that it is the way that distance is measured that makes it seem less:

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it's not a "real" contraction in the sense that there is no internal tension; you could think of it as an "artefact" of how we *define* distance between two points
 

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