Object Shortening: Causes & Similarities to Time Dilation

[scott_alexsk]

Hello,
I just want to clarify something. Why do objects shorten as they travel faster. Is this similar to time dilation except with spatial demensions?
Thanks,
Scott

 

[HallsofIvy]

It is not just objects that "shorten". Space itself contracts along the direction of travel.

 

[mitchellmckain]

Hello,
I just want to clarify something. Why do objects shorten as they travel faster. Is this similar to time dilation except with spatial demensions?
Thanks,
Scott

Well you can ask why endlessy, but I can explain a few things. First of all motion is relative so for an observer on that moving object it is you that is moving and not him. So while you think the object is shortened, he thinks it is you that is shortened and not him.

This seems like a contradiction but it is not. The fact is that you and this observer on the moving object see the entire universe very differently. One of the key differences is that you and he do not interpret the events in the universe as occurring in the same order. For example, suppose you see a star 10 light years in front of you (that is 10 light years in the direction that the object is moving) going nova at the same time as you see a star 10 light years behind you (10 light years in the direction opposite the way the object is moving) also going nova. Since you know that it takes 10 years for light to travel 10 light years distance you know that the two novas occurred at the same time 10 years ago, right? Well the observer on the moving object would not agree. You see from his point of view the two stars are moving. One is moving towards him and the other is moving away from him. So even though he sees the novas at the same time just like you, he knows that the light from the nova of the star coming toward him must have traveled farther than the light from the nova of the star going away from him. This is because even though at present time both stars are equally distant, the star coming toward him was farther away just a short time ago and the star going away from him was closer. Therefore, he concludes that the nova of the star coming toward him happed first before the nova of the star going away from him.

For me it always help keep things straight to put numbers to these things so suppose the object is moving 86.6% of the speed of light. Then according to his calculations the light from the nova of the star coming toward him left that star 37.32 years ago when that star was 37.32 light years away. The light from the nova of the star going away from him left that star 2.68 years ago when that star was only 2.68 light years away. So while you think the two novas occurred at the same time, he thinks that they happened 34.64 years apart. During the 2.68 years that the light from the receding star is traveling towards him the star moves .866 times 2.68 = 2.32 light years farther away so that it is now 2.32 + 2.68 = 5 light years away. During the 37.32 years while the light from the approaching star is traveling towards him, the star moves .866 times 37.32 = 32.32 light years towards him so that it is now 37.32 - 32.32 = 5 light years away.

But wait a minute. For you the two stars were 20 light years apart, while for him the two stars are only 10 light years apart. The fact is that for him, you and the two stars are moving at 86.6% of the speed of light and so you, the two stars and all the spaces in between are all shorter by a factor of two. For you it is the the object which is moving and which is shorter by a half. If there are two more stars which are not moving from his point of view, 20 light years apart, 10 light years away in each direction, then you would see these stars as moving and only 10 light years apart. It seems crazy and contradictory but contradictions are resolved by this fact that you and he do not see events occurring in the same order.

To see this more clearly let's label the first two stars Af and Ar, and label the second two stars Bf and Br. Then you see this,

Ar...(5 ly)...Br->...(5 ly)...you...(5 ly)...Bf->...(5 ly)...Af

while he sees this,

Br...(5 ly)...<-Ar...(5 ly)...him...(5 ly)...<-Af...(5 ly)...Bf

This is possible because, while for you Br has already passed Ar, for him this has not happened yet, and while for him Af has already passed Bf, for you this has not happened yet. All the events which have already happened to your rear (Br passing Ar and Ar going nova), for him have happened more recently (Ar going nova) or haven't even happened yet (Br passing Ar). All the events to your front, one of which has not happened yet, have already happened (Af passing Bf) or happened long ago (Af going nova). So in sense you could say that the observer on the "moving" object sees to the rear what you would call your past and he sees to the front what you would call your future. In fact as he looks at you, your front side is slightly in the future compared to your rear side, and during that time difference your front side has traveled closer to your rear side, and so he calculates you to be shorter from front to rear.

This is not what he sees, because that is subject to a further distortion due to the fact the light which he sees you by takes time to travel to his eye. The light from your farther side has to travel a little farther than the light from your closer side and at 86.6% of the speed of light, you move a significant amount during that time. The result is that when you are in front of him moving toward him you actually appear elongated and it is only when you are behind him traveling away from him that you appear shorter (even shorter than half).

 

[scott_alexsk]

I appreciate that. So is it that the object is actually shortening, or is it that it appears to shorten for the observer. I understand either person will picture this, but for one is the person actually shorter in spatial demensions. Or does this only have to do with light from one end of the person reaching the viewer first and I am just complicating things? Also at the point person 1passes directly in front of person 2, with person one oriented perpindicular to person ones path. At the exact moment he passes in front of him will he appear normal lenght? Does the person become shorter as he gets closer, even though he is longer than what he really is?
Thanks,
Scott

 

[mitchellmckain]

I appreciate that. So is it that the object is actually shortening, or is it that it appears to shorten for the observer. I understand either person will picture this, but for one is the person actually shorter in spatial demensions. Or does this only have to do with light from one end of the person reaching the viewer first and I am just complicating things?

The object is shortening according to his calculations after he takes into account the different times that the light takes to get to him from different parts of the object (called the aberration of light). If he does not take this into account the object actually appears elongated when in front of him, and even more shortened when behind him.

Also at the point person 1passes directly in front of person 2, with person one oriented perpindicular to person ones path. At the exact moment he passes in front of him will he appear normal lenght?

Yes due to the different times light takes to get to him from the different parts of the object, at this point the object will appear to be normal length but rotated (like seeing the object from a direction that more in front of him). In fact, he sees it as being farther in front of him. You don't see things where they are but where they were when the light we see them by left them. But if he takes into account the problem of light traveling from different parts of the object (the aberration of light) he will calculate that the object is actually shortened.

If he waits until the object actually appears to be passing him, when it is actually already behind him, then it appears shortened.

Does the person become shorter as he gets closer, even though he is longer than what he really is?

We always calculate an object or person which is moving to be shortened in exactly the same way and by the same amount depending only on its velocity but because of the aberration of light it appears elongated in front of us and even more shortened than what we calculate when it is behind us. An observer on the object never thinks that he is enongated or shortened, instead he calculates us to be shortened and sees us going from elongated to shortened as he passes us.

One does not look (or calculate to be) shorter because the other is longer in any way. It is all about seeing different parts of an object at different times it its history. If there are little clocks all over the object the clocks would not all read the same time, and then you would realize that the tail end is closer to the front end simply because it has moved farther already.

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[JM]

Understanding Special Relativity

It is not just objects that "shorten". Space itself contracts along the direction of travel.

To Halls of Ivy,
I note that in your "read this" item that this forum is for those who want to increase their understanding of Special Relativity. In that spirit I offer the following comments.
It can be shown that the Lorentz Transforms can be derived using ordinary reasoning, math, and physics of the undergraduate college level. This analysis identifies two mechanisms that are used to satisfy the Postulate of Constant Light Speed. Using the mechanisms as a basis, the phenomena of slow clocks, shrinking objects, and the twin paradox are explained ( for small but non-zero values of v/c). This is not new theory, but is an exploration of the theories already published by Einstein.
I have described this analysis in a book. It is too extensive to publish on-line, and I wonder how to make it available. Do you think your viewers would be interested? Any comments?
I will rely on you to place this on the appropriate thread.

 

[jtbell]

So is it that the object is actually shortening, or is it that it appears to shorten for the observer.

Consider the following non-relativistic situation. If someone stands in front of you and holds up a meter stick at right angles to your line of sight, you perceive the full length of the meter stick. If the other person rotates the meter stick horizontally, 60 degrees from its original orientation, so that it forms a 30-degree angle with your line of sight, it will "appear" to you to be only a half meter long (especially if you close one eye so as to eliminate your sense of "depth perception").

I think that people would generally agree that the rotated meter stick only "appears" to be a half-meter long, and that it is "really" still one meter long. Nevertheless, this "apparent" shortening can have physical consequences! For example the person holding the rotated meter stick can walk towards you through a door that is only a half meter wide (plus a little bit ).

Similarly, length contraction of a moving object can have real physical consequences, although one can legitimately argue that it only "appears to shorten". It's more than a simple illusion.

 

[scott_alexsk]

Thanks. So even though the object still maintains its orginal demensions, from another frame of reference it can appear completely different and as a result it can do things not orginally thought.
-Scott

 

[selfAdjoint]

Thanks. So even though the object still maintains its orginal demensions, from another frame of reference it can appear completely different and as a result it can do things not orginally thought.
-Scott

It retains its original dimensions in its own rest frame which it has, if it has mass. But that frame is no better, and no worse, for saying "what happened" than any other. The "foreshortened view" is just as valid as the "straight-on" view. Just as Renaissance painters had to learn to paint things correctly in perspective, since there was no way to see without it, so thinkers today have to learn to think with relativity, since it is confirmed thousands of times daily by objective experiments.