# 4 length contraction questions.

## Main Question or Discussion Point

If I was traveling close to the speed of light and passed a hotdog outside, the hotdog would appear smaller to me compared to the hotdogs I remember eating on earth correct?

If I was traveling close to the speed of light with a hotdog in my hand and held it right in front of my pants, as I passed another hotdog outside, would it appear to me that the two hot dogs were different sizes? The one outside would contract but the one with me inside would be as I always remember the traditional hotdog correct?

If I was traveling close to the speed of light and passed a seemingly smaller than usual hotdog, reached my hand out of the window and grabbed the hotdog and pulled it inside, would the hotdog appear to expand and grow to a normal hotdogs size?

If someone was traveling at the exact speed of light would the distance between them and any object directly in front of them be zero, or just a very small number? Or am I’m off completely.

Thanks for listening,

S

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russ_watters
Mentor
Originally posted by syano
Or am I’m off completely.
Yeah, that. You're trying to compare things in one frame of reference to those in another in a way that isn't allowed. The hotdog outside your window is close to your frame of reference and would look pretty much normal - unless it was going a lot slower in which case you wouldn't get a good look at it anyway.

russ is right. But for the sake of argument let's say you are travelling much faster than the hot dog and can manage to measure it (or that you are travelling a bit faster and have a crazy accurate ruler) by length contraction your ruler would get smaller so the shrinking ruler would display a longer hot dog.

The hotdog I pass is stationary (make it relative to whatever you want as long as its not my spaceship) For all I know me and my spacecraft are approaching the hotdog at near the speed of light or the hotdog is approaching me at near the speed of light.

I used a hotdog in hopes to rule out the need to measure it. I have a good idea, or memory, on what a hotdog looks like. And wanted to know how obscure I would see it under the circumstance in the original post.

Thanks,

S

Oh, well that's for the best since what I said is not only wrong but incredibly stupid :) I don't know what made me think the ruler would seem contracted in your frame...

Janus
Staff Emeritus
Gold Member

Originally posted by russ_watters
Yeah, that. You're trying to compare things in one frame of reference to those in another in a way that isn't allowed. The hotdog outside your window is close to your frame of reference and would look pretty much normal - unless it was going a lot slower in which case you wouldn't get a good look at it anyway.
I believe the idea is that you are traveling at relativistic speeds with respect to the hot dog outside your window, and that you are capable of taking snapshot of the the two hot dogs while they pass each other with a extremely high speed camera.

In which case, the outside hot dog would indeed measusre as smaller.

I like ze biiig hot dog..

pmb
Originally posted by syano
If I was traveling close to the speed of light and passed a hotdog outside, the hotdog would appear smaller to me compared to the hotdogs I remember eating on earth correct?
So long as the hotdogs are lying parallel to the relative motion of moving and stationary hotdogs. See

http://www.geocities.com/physics_world/sr/lorentz_contraction.htm

If I was traveling close to the speed of light with a hotdog in my hand and held it right in front of my pants, as I passed another hotdog outside, would it appear to me that the two hot dogs were different sizes?
Yes. That is what Lorentz contraction means. When you comare two objects which have the same length when at rest then the one which is moving, as described above, will be measured to be shorter. That is why you should stay stationary if you want to impress your girlfriend. :-)

The one outside would contract but the one with me inside would be as I always remember the traditional hotdog correct?
Yes.

If I was traveling close to the speed of light and passed a seemingly smaller than usual hotdog, reached my hand out of the window and grabbed the hotdog and pulled it inside, would the hotdog appear to expand and grow to a normal hotdogs size?
Yes.

If someone was traveling at the exact speed of light ...
Sorry but that can't happen so the question is meaningless.

Pete

There has been some stuff written about this changing frames wierdness. (pulling the stationary hotdog into the spaceship) Do a search on the ladder in the barn.

-Allday

pmb
Originally posted by Allday
There has been some stuff written about this changing frames wierdness. (pulling the stationary hotdog into the spaceship) Do a search on the ladder in the barn.

-Allday
When someone changes the speed of an object then what happens is that, even though all parts may change their speed "at the same time" they don't do so "at the same time" in another frame since "at the same time" is not Lorentz invariant.

Pmb

If I were to pass all those hotdogs, I'd get my intestines checked.

Njorl
Now suppose you had a roll that was too short for your hot dog. You swing past Lorentzo's Relativistic Drive Thru Hot Dog Stand fast enough so that the wiener looks short enough to fit in the roll. You stick your roll out the window and snap it down on a wiener without slowing down, but when you pull it into the car, the ends stick out. Neat, huh?

Njorl

krab
The view (that an object is simply shortened by Lorentz contraction) is not correct, and was corrected in 1959. It is generally known now that such an object appears rotated. Unfortunately, old errors die hard.

http://35.8.247.219/home/modules/pdf_modules/m44.pdf This is the best explanation I've seen.

Last edited by a moderator:
pmb
Originally posted by krab
The view (that an object is simply shortened by Lorentz contraction) is not correct, and was corrected in 1959.
That is incorrect. You've misunderstood that article. That is not what the author meant. To make sure I understood him I e-mailed him to double check.

The article by Terrell does *not* say that observers don't "observer" Lorentz contractions. It states that observers don't "see" a Lorentz contraction. Read Terrell's paper at the end of the article. Observering length has to do with simultaneous measurements while seeing has to do with optics.

The author of the article you just linked to, i.e. the one I e-mailed, clearly states
5a. Modifcation Due to Lorentz Contraction. Using relativity,(2)
one finds that a moving length in the direction of motion becomes contracted from its "rest-frame" or proper value L_o to L(v) = L_o*sqrt[1-(v/c)^2]. Side AD of the cube in Fig. 1 has its entire length in the direction of motion. Therefore the Lorentz contraction modifies Fig. 5 in the manner shown in Fig. 6.
For the standard rigorous derivation of Lorentz contraction see

http://www.geocities.com/physics_world/sr/lorentz_contraction.htm

Pete

krab
Originally posted by pmb
That is incorrect. You've misunderstood that article. That is not what the author meant. To make sure I understood him I e-mailed him to double check.

The article by Terrell does *not* say that observers don't "observer" Lorentz contractions.
Neither did I. Read what I wrote again. By "simply shortened" I meant the naive point of view that the observer would see the same hot dog he sees when the hot dog is at rest, only shortened in the direction of motion.

pmb
Originally posted by krab
Neither did I. Read what I wrote again. By "simply shortened" I meant the naive point of view that the observer would see the same hot dog he sees when the hot dog is at rest, only shortened in the direction of motion.
You're comment is wrong as it stands. Nodody was talking about seeing and nothing in your quote indicated it.

The rod is shortened. If your "simple" qualifier was supposed to make your comment clear about the optics then it wasn't clear at all. Nothing in this thread was about what the observer sees. We were talking about what the length "is." That means what is measured.

Pmb

Thanks for the conversation guys! And thanks pmb for also noticing the possible dilemma when passing your girlfriend in another ship lol!

When I asked the question about going the exact speed of light I had a feeling I was taking it a bit overboard. So I would like to reword the 4rth question and try again. If it is still too implausible just shoot it down again :-)

Rewording attempt of question 4:
If a piece of light had eyes, a brain and reasonable thought and was traveling the exact speed of light would the distance between it and any other object directly in front of it be zero or just a very small number?

Another Rewording attempt of question 4:
If I was traveling at .999c towards the star Vega (I think it’s about 26 light years away) would the distance between me and Vega be a very small number? Would it be fair to say the number could be less than, or close to, one meter?

I think what I’m trying to get at is this:
I can comprehend Lorentz Contractions when passing a fast moving object or a fast moving object passing me; but I am not sure how that applies to objects I am traveling to and if that distance contracts as well.

Thanks again for the clarification and conversation, much appreciated,

S

Janus
Staff Emeritus
Gold Member
Originally posted by syano
Thanks for the conversation guys! And thanks pmb for also noticing the possible dilemma when passing your girlfriend in another ship lol!

When I asked the question about going the exact speed of light I had a feeling I was taking it a bit overboard. So I would like to reword the 4rth question and try again. If it is still too implausible just shoot it down again :-)

Rewording attempt of question 4:
If a piece of light had eyes, a brain and reasonable thought and was traveling the exact speed of light would the distance between it and any other object directly in front of it be zero or just a very small number?

Another Rewording attempt of question 4:
If I was traveling at .999c towards the star Vega (I think it’s about 26 light years away) would the distance between me and Vega be a very small number? Would it be fair to say the number could be less than, or close to, one meter?

I think what I’m trying to get at is this:
I can comprehend Lorentz Contractions when passing a fast moving object or a fast moving object passing me; but I am not sure how that applies to objects I am traveling to and if that distance contracts as well.

Thanks again for the clarification and conversation, much appreciated,

S
Yes, the distance between objects you are traveling between contracts just like anything else. It has to in order to compliment time dilation.