Can a spaceman survive length contraction?

[asprung]

It is said that the space twin ages slower then when he started his trip and slower than his earth twin.

[swansont]

It is said that the space twin ages slower then when he started his trip and slower than his earth twin.

 

And the earth twin ages slower, too — they each see the other's clock as sunning slow. That symmetry is broken when one of them accelerates into another inertial frame. As long as there is no acceleration, each of them thinks their own clock is right and the other's clock is slow.

[asprung]

If time compression does not effect his ageing rate in his owne frame how does he end up younger than he would have been if he stayed on earth?

[Janus]

If time compression does not effect his ageing rate in his owne frame how does he end up younger than he would have been if he stayed on earth?

 

Due to length contraction he views the distance of the trip as being shorter.

 

Say he was traveling towards a star 7 light years away at 0.99c. For a person on the Earth, he would age 1/7th as fast and only age about 1 year, during the 7 years that pass on Earth.

 

As far as he is concerned he ages normally, but the distance between earth and the star has contracted to 1 ly, and thus it takes him about 1 year to cross the distance at 0.99c according to him.

 

Thus from both the Earth point of view and his, he arrives at the star having aged 1 yr, they just disagree as to why this is the case. Earth says it is because he aged slower, and he says it is because the distance was shorter. Either explanation is equally valid (There is no one right explanation.)

Edited May 16, 2009 by Janus

[NowThatWeKnow]

Deleted

[asprung]

Does he arrive shorter?

[J.C.MacSwell]

Does he arrive shorter?

 

LOL. If you are having us on that is brilliant.

 

 

Answer:

 

If he arrives at speed with is body aligned in the direction of travel (effectively a fly by)...yes.

 

If he arrives by coming to rest...no.

[iNow]

Does he arrive shorter?

 

Relative to whom/what?

[Kyrisch]

Could length contraction viewed from other time frames cause damage? Stranger things seem to happen.

 

Something else that should have been pointed out earlier. Everything in the direction of travel will be length contracted as observed by the rest frame, including each individual molecular bond-length, so there would obviously be no structural damage.

[padren]

Hope I am not adding to the confusion, but there's something I'd like to understand:

 

Say you have bomb, that is in a perfect cube, and the detonation is triggered due to physical distortion. Just as a mechanical visual, say inside the cube (viewed from the side, as a square) half way along the bottom, is a laser that shoots inside at 45 degrees, to hit the center of the left wall, and a mirror, to reflect it to the top, and another mirror, to reflect it to the right wall, and another mirror, that hits a "receptor" positioned to intercept it right next to the beam generator on the bottom.

So, you have a box, and a light beam bouncing around touching the exact middle of each side. If the beam is not detected by the receptor, it blows up.

 

Now, from the bomb's frame - it's at rest, there is no length distortion, and the bomb is happy not to explode. From an observer's frame, it's contracted due to it's relative velocity, and no longer a cube causing the light beam to fail to touch the receptor.

 

Now, I assume the observer would not see the bomb explode - instead, it would see the light inside the box also distort. So I guess what I am asking is, how does the real observations made by the observer, impact the observer's frame? I seems the only logical explanation is from the observer's frame, all physics inside the observed frame all also appear to react in a "distorted way" thus allowing things such as the bomb not going off when it should.

 

But then we throw in something like say - the traveling bomb is just large enough to fully eclipse a light source in the background unless it's distorted to the observer. I take it that the observer does not see the light source fully eclipsed when the object moves past.... but according to the object's perspective, it would see the observer fully "eclipsed" and in the dark for a moment?

 

Then there is the issue of how many photons hit the object as it passes - depending on if it's compressed or not. Is it safe to assume, since the light is stationary to the observer, but not to the object traveling, that the light source then appears distorted to the traveling object, and as a result only has 'x' photons to shed, which happens to exactly match up with the photons observed by the original stationary observer, who sees the photon count being the result of the object's speed vs. the stationary light?

 

I've never been able to fully wrap my head around relative frames - but I assume it's not unlike the distorted topography of space due to gravity described by the old "bowling ball on a foam mattress" analogy. That is, you can paint a grid on it, then place a bunch of weights and "distort it" but all the lines still line up in the end. If you don't "see" the whole distorted grid, and just measure 4 points near a mass and measure 4 points far from the mass, you'd see the squares have different sizes and ask "how can they both be right?" and why you don't end up with a bunch of broken lines, since a bunch of squares of slightly different sizes can't possibly make a perfect continuous grid.

Thankfully, we can see the grid example in it's entirely, and we can say "ah ha" and easily conceptualize it. I think relative frames operate the same way (abstractly, not literally), but are much harder to visualize, so when you just take measurements from one or another it becomes really hard to see how it could all add up together in the big picture.

 

Take the "two clocks" example where one is put in orbit and flies around the earth a lot, and comes back slightly slower, having aged less than the clock that was relatively stationary:

 

A question like "How many photons hit the stationary clock vs the moving clock, since both were exposed to the same sunlight?" seem to imply either one frame is right and the other is wrong, or both are broken - when in reality, because of all the factors that get distorted, observations from either frame will result in consistent observations. Since it can't be visually described on a nice little grid painted mattress, it's harder to see how it works out, but mathematically and physically, it still does.

 

Do I have that right?

[swansont]

An event has to either happen or not happen — the only discrepancy can be when it happened. So if the bomb is not triggered in the rest frame, it is not triggered — how can it? Relativity does not cause objects themselves to physically compress, it cause spacetime to change, and it because of that that time and length change.

 

So you can't make something e.g. miss a target solely by moving into another frame. If there is a distortion of the trajectory, the target gets moved as well. If it hits, it hits in every frame. If it misses, it misses in every frame.

[asprung]

The spaceman ends his trip ageing at a slower rate then when he started. This occurs in his own time frame in which if I understand correctly no such change should be observed by him.

[swansont]

The spaceman ends his trip ageing at a slower rate then when he started. This occurs in his own time frame in which if I understand correctly no such change should be observed by him.

 

In his own frame he sees things normally. When he undergoes his acceleration he will notice other clocks readjusting at a very fast pace, such that a very long time will have elapsed by those clocks .

[padren]

An event has to either happen or not happen — the only discrepancy can be when it happened. So if the bomb is not triggered in the rest frame, it is not triggered — how can it? Relativity does not cause objects themselves to physically compress, it cause spacetime to change, and it because of that that time and length change.

So essentially, what gravity does to space, relative velocity per-frame-perspective does to spacetime?

 

So you can't make something e.g. miss a target solely by moving into another frame. If there is a distortion of the trajectory, the target gets moved as well. If it hits, it hits in every frame. If it misses, it misses in every frame.

 

So really, when we look at ladders from different frames or any such event that could raise an apparent contradiction - in actuality this is simply caused by distortions in space/time that all still add up to a single, consistent set of variables.

 

Just a quick question: I recall my physics teacher in high school saying as you approach the speed of light, it takes more energy to accelerate at a constant rate, because you get heavier, and you'd eventually get so heavy you'd collapse into a black hole. Is that true/false/unrelated to issues of frame or oversimplified? If it's too off topic for here I apologize.

[prodigenius]

The biggest mental leap from classical mechanics to relativity is getting over the concept of universality - that time, space, and everything in them are not the same from everyone's point of view. There is no universal "now." But there aren't paradoxes, actually. One of my favorite ones is a guy running into a 30ft barn with a 30 foot stick at 3/5c, and once he's inside, the barn door closes behind him. The guy sitting in the barn says he fits - the guy and the stick are length contracted and the barn stays at 30ft, so he fits in fine. The running guy says he can't fit - he has a 30 ft stick and the barn is length contracted shorter - there's no way he can fit. Even if the 2 observers can't agree on the length of the stick, they have to agree on whether or not it fits. You can't have one person saying the door closes around the stick and one guy saying the door can't close - they have to agree on this event. Can you figure out who is right and why?

 

It's a little wacky at first, but understand that concept and a lot of relativity falls in to place. The solution to this problem isn't math intensive, but it's beautiful. There are books that explain it far better than anyone in this thread, so I suggest reading about it.

[J.C.MacSwell]

Just a quick question: I recall my physics teacher in high school saying as you approach the speed of light, it takes more energy to accelerate at a constant rate, because you get heavier, and you'd eventually get so heavy you'd collapse into a black hole. Is that true/false/unrelated to issues of frame or oversimplified? If it's too off topic for here I apologize.

 

The bold is false. You are in other reference frames relative to which you are close to the speed of light, yet you are in no danger of collapsing into a black hole in those frames any more than you are in your rest frame.

[Sisyphus]

The "constant acceleration" bit is tricky, too. It takes more and more energy to maintain constant acceleration relative to some other, inertial frame. If you are given an infinite fuel rocket and launch at a constant thrust away from the Earth, in the rest frame of the Earth your acceleration will taper off as you approach C, and you will get steadily more massive. But from your own perspective, your velocity is always zero, and you can keep adding energy indefinitely at the same rate, and you won't notice any change.

[NowThatWeKnow]

...But from your own perspective, your velocity is always zero, and you can keep adding energy indefinitely at the same rate, and you won't notice any change.

Except you will get to your destination faster. Andromeda galaxy in less then 30 years anyone?

[swansont]

So essentially, what gravity does to space, relative velocity per-frame-perspective does to spacetime?

 

It's probably a mistake to separate the two (space and spacetime). Gravity slows time as well as curving space. However, being stationary in a gravity field is an accelerating frame of reference, so we know for sure whose spacetime is being changed.

 

For flat spacetime, the length and time transformations are reciprocal. Once you get used to it, it's easy to see how the effects compensate for each other to give an overall consistent picture.

 

So really, when we look at ladders from different frames or any such event that could raise an apparent contradiction - in actuality this is simply caused by distortions in space/time that all still add up to a single, consistent set of variables.

 

Right. You agree on event happening/not happening, but you won't agree on simultaneity. i.e. everyone must agree that the barn door shuts, but the different observers disagree on when the other door opens, or whether the ladder was completely inside the barn, since those are issues of length and timing.

Edited May 18, 2009 by swansont

[Sisyphus]

Except you will get to your destination faster. Andromeda galaxy in less then 30 years anyone?

 

Right, right. I should say, you won't notice any difference in yourself. You will notice the rest of the universe changing quite a bit, however. Like the Andromeda Galaxy being flattened, multiplied in mass, only a few lightyears away, blueshifted into all nasty radiation, and hurtling towards you at nearly the speed of light. Which is a pretty big change.

[GDG]

It's more than just how he looks, though, which I think is the source of most of the confusion in this thread, so it should be repeated. It affects how he is in another frame. It is more than merely an illusion. It's exactly as real as time compression - in fact, they're two sides of the same phenomenon. Just as in the twin paradox, they really are different ages at the end, in the ladder paradox, the length contracted ladder really does fit inside the barn that's otherwise too short for it. Even though the twin doesn't himself experience anything unusual, and neither does the ladder.

 

I think you're right that this is the source of the confusion. If you and the astronaut are in different reference frames, every measurement you make of him from your reference frame will differ from his own measurements made in his own reference frame (including time and length). To the extent he "is" what you measure, you are correct. I think most of us non-physicists limit the concept "is" to whatever the astronaut experiences in his own rest frame. This, I believe, is the source of the confusion. Certainly, the measurements in both frames are real and repeatable, but measurements made in one frame do not affect the measurements made in another frame.

[padren]

Right. You agree on event happening/not happening, but you won't agree on simultaneity. i.e. everyone must agree that the barn door shuts, but the different observers disagree on when the other door opens, or whether the ladder was completely inside the barn, since those are issues of length and timing.

 

Perhaps I am just confused on how everything manages to ultimately match up consistently in the end, but if you had doors on either side of the barn, and someone outside and someone inside disagreed on when which were open - either both are open at the same time and light can pass through the barn, or the doors aren't open at the same time and light can't.

 

Are you saying both will agree that both are open or closed in synchronicity or not, but disagree on the time, or will the two parties disagree on the timing of both, allowing one to see the doors close in synchronicity and the other not?

 

I hope I am not belaboring it - but just want to be sure - I assume you are saying they disagree on the 'when' but it will be the 'when' of when both doors open/close in synchronicity.

[J.C.MacSwell]

Perhaps I am just confused on how everything manages to ultimately match up consistently in the end, but if you had doors on either side of the barn, and someone outside and someone inside disagreed on when which were open - either both are open at the same time and light can pass through the barn, or the doors aren't open at the same time and light can't.

 

Are you saying both will agree that both are open or closed in synchronicity or not, but disagree on the time, or will the two parties disagree on the timing of both, allowing one to see the doors close in synchronicity and the other not?

 

I hope I am not belaboring it - but just want to be sure - I assume you are saying they disagree on the 'when' but it will be the 'when' of when both doors open/close in synchronicity.

 

Not at all. That is the key. One sees the doors close in synchronicity and the other not.

[padren]

Not at all. That is the key. One sees the doors close in synchronicity and the other not.

 

Something else has to be in the equation then: I mean, either light is shining through the two open barn doors from a light source behind it (because they are both open at the same time) or it is not. If there was a bomb that was set to go off with a light sensitive trigger it either blows up or it doesn't. One person can't see the light hit the trigger and the other not, so how is this reconciled?

[swansont]

Something else has to be in the equation then: I mean, either light is shining through the two open barn doors from a light source behind it (because they are both open at the same time) or it is not. If there was a bomb that was set to go off with a light sensitive trigger it either blows up or it doesn't. One person can't see the light hit the trigger and the other not, so how is this reconciled?

 

It takes time for the light to pass through the barn. Even if they are opened out of sync, if that time difference is less than L/c, light will get through.