Length Contraction: Exploring the Possibility of Black Holes at High Speeds

[Matt Fenwick]

TL;DR Summary

Length contraction: is it real? Black hole thought experiment.

If I am traveling in my spacecraft at .99999999 percent the speed of light past a star, then according to the equation of length contraction a star with 4x or more solar mass would contract along the line of motion according to my frame of reference by an amount of over Length naught (8*10-E), thus producing a black hole. Does anyone think this really happens? Perhaps, if you consider the speed of light constant in all frames of reference then it is velocity that is undergoing a transformation in accordance with your slower clock.

 

[Orodruin]

thus producing a black hole

No, this inference is not correct.

 

[PeroK]

If I am traveling in my spacecraft at .99999999 percent the speed of light past a star, then according to the equation of length contraction a star with 4x or more solar mass would contract along the line of motion according to my frame of reference by an amount of over Length naught (8*10-E), thus producing a black hole.

This is a common misconception. You can't turn star into a black hole simply by travelling very fast. For example, if we released a very high energy particle from CERN and fired it past the sun at nearly the speed of light, then the sun would be unaffected. It definitely wouldn't turn into a black hole.

 

[phinds]

Length contraction: is it real?

You, as you read this, are traveling at almost the speed of light relative to a particle in the CERN accelerator. Do you feel any heavier? Do you feel contracted in any dimension?

 

[Ibix]

Does anyone think this really happens?

No, because physics doesn't work that way. It can't, because the picture you describe is inconsistent: a person at rest with respect to the star would see a normal glowing star, but your traveller would see a black hole. They can't both be right.

Stars don't collapse because of the radiation pressure (among other things) from their fusion reactions. Your traveller would, indeed, see the star contracted in one direction (or at least measure it so - what they would actually see is more complicated), but would also see an anisotropic radiation pressure that was sufficient to stop collapse. Furthermore, the traveller would see a non-spherically symmetric mass, which is enough to invalidate a simple "must be a black hole if contained within its Schwarzschild radius" analysis - that shortcut only works if the mass is spherically symmetric in your coordinates.

So no, the traveller would not see a black hole. And there would be plenty of reasons for this not to be surprising.

 

[Matt Fenwick]

You, as you read this, are traveling at almost the speed of light relative to a particle in the CERN accelerator. Do you feel any heavier? Do you feel contracted in any dimension?

Of course I don't feel heavier or contracted. Nor do I believe the star would magically produce any unusual opposing forces. I think the formula is wrong. There are two velocities. One for the chosen non moving reference frame (the hypothetical star you have left, the one you are heading towards, and the one you are passing). The second velocity being you in the spaceship.

 

[Ibix]

I think the formula is wrong.

What, you think the Lorentz transforms are wrong? Here's an introduction to the evidence they're not. You do need more sophisticated means to properly analyse a star, but as a first approximation telling you the star will look like a pancake, they're fine here.

 

[Orodruin]

I think the formula is wrong.

What formula?

 

[Dale]

I think the formula is wrong.

What formula? Chances are that the formula is right you are just misapplying it. But without clarity about what formula you are talking about I cannot say for sure

TL;DR Summary: Length contraction: is it real? Black hole thought experiment.

If I am traveling in my spacecraft at .99999999 percent the speed of light past a star, then according to the equation of length contraction a star with 4x or more solar mass would contract along the line of motion according to my frame of reference by an amount of over Length naught (8*10-E), thus producing a black hole. Does anyone think this really happens?

It is not a prediction of relativity that it should happen. If you believe that this is a prediction of relativity then you have misunderstood something

 

[phinds]

I think the formula is wrong.

Personal theories are prohibited here on PF. Particularly ones that make no sense.

 

[jbriggs444]

TL;DR Summary: Length contraction: is it real?

Back to the original post. Exactly what do you mean by "real"?

Do you mean "measurable"?
Do you mean "invariant"?

If I draw two parallel lines on a piece of paper, is it "really" the case that the distance I measure between the two lines depends on the angle at which I hold my ruler?

 

[Orodruin]

If I draw two parallel lines on a piece of paper, is it "really" the case that the distance I measure between the two lines depends on the angle at which I hold my ruler?

I want to underline this because the meaning may otherwise be lost to the OP. What is described here is the normal space equivalent of length contraction in spacetime.

 

[Matt Fenwick]

What formula? Chances are that the formula is right you are just misapplying it. But without clarity about what formula you are talking about I cannot say for sure

It is not a prediction of relativity that it should happen. If you believe that this is a prediction of relativity then you have misunderstood something

Lorentz Transformation with respect to length contraction. It seems to imply a real conversation of length at the expense of an unchanging velocity regardless of reference frame.

 

[Ibix]

Lorentz Transformation with respect to length contraction.

I strongly recommend reading posts #11 and #12. They give a good insight into how length contraction happens.

It seems to imply a real conversation of length at the expense of an unchanging velocity regardless of reference frame.

I have no idea what you think this means.

 

[Matt Fenwick]

Back to the original post. Exactly what do you mean by "real"?

Do you mean "measurable"?
Do you mean "invariant"?

If I draw two parallel lines on a piece of paper, is it "really" the case that the distance I measure between the two lines depends on the angle at which I hold my ruler?

What I mean by real is: does the space between atoms/molecules shrink, do the atoms shrink at the expense of repulsive forces, or is there some sort of magical bubble of spacetime that shrinks as it follows the object undergoing length contraction?

 

[PeroK]

What I mean by real is: does the space between atoms/molecules shrink, do the atoms shrink at the expense of repulsive forces, or is there some sort of magical bubble of spacetime that shrinks as it follows the object undergoing length contraction?

You're stumbling about in the dark here. There is nothing magical about SR, but you have to put some effort into understanding it.

 

[Ibix]

What I mean by real is: does the space between atoms/molecules shrink, do the atoms shrink at the expense of repulsive forces, or is there some sort of magical bubble of spacetime that shrinks as it follows the object undergoing length contraction?

The object is four dimensional. You "see" a 3d slice through it. The "angle" of that slice depends on the velocity of the object with respect to you. Length contraction is thus the Minkowski spacetime equivalent of slices of sausage being circular or elliptical depending on the angle you slice at.

Nothing shrinks - you are just looking at different 3d parts of a 4d whole. The forces between atoms do also transform, since charged particles stationary in one frame are moving in another.

 

[Sagittarius A-Star]

What I mean by real is: does the space between atoms/molecules shrink, do the atoms shrink at the expense of repulsive forces

The space between atoms (length-contracted), the thickness of atoms (length-contracted), the forces and the electromagnetic field are transformed by the Lorentz transformation in a consistent way.

Einstein wrote regarding the "reality" of length contraction:

The question as to whether length contraction really exists or not is misleading. It doesn't "really" exist, in so far as it doesn't exist for a comoving observer; though it "really" exists, i.e. in such a way that it could be demonstrated in principle by physical means by a non-comoving observer.[22]

— Albert Einstein, 1911
Einstein also argued in that paper, that length contraction is not simply the product of arbitrary definitions concerning the way clock regulations and length measurements are performed. He presented the following thought experiment: Let A'B' and A"B" be the endpoints of two rods of the same proper length L0, as measured on x' and x" respectively. Let them move in opposite directions along the x* axis, considered at rest, at the same speed with respect to it. Endpoints A'A" then meet at point A*, and B'B" meet at point B*. Einstein pointed out that length A*B* is shorter than A'B' or A"B", which can also be demonstrated by bringing one of the rods to rest with respect to that axis.

Source:
https://en.wikipedia.org/wiki/Length_contraction#Reality_of_length_contraction

 

[Nugatory]

Lorentz Transformation with respect to length contraction. It seems to imply a real conversation of length at the expense of an unchanging velocity regardless of reference frame.

The Lorentz transformations imply more than just length contraction. There's also time dilation and (often underemphasized in pop-sci treatments) the relativity of simultaneity. We always have to consider all three to get an internally consistent picture of what's going on - and indeed most relativity "paradoxes" come from overlooking relativity of simultaneity.

The length of something is, by definition, the distance between where the ends of that something are at the same time. Relativity of simultaneity means that "at the same time" is frame dependent and therefore that the positions of the ends at the same time and the distance between them will be different when we use different frames. So what does it mean to say that the length is "really" contracted?

 

[Dale]

Lorentz Transformation with respect to length contraction. It seems to imply a real conversation of length at the expense of an unchanging velocity regardless of reference frame.

The Lorentz transformation is exceptionally well confirmed experimentally. However, your understanding of black holes is wrong. A fast moving star does not become a black hole. That is not a prediction of relativity.

 

[PeterDonis]

What I mean by real is: does the space between atoms/molecules shrink, do the atoms shrink at the expense of repulsive forces, or is there some sort of magical bubble of spacetime that shrinks as it follows the object undergoing length contraction?

None of the above.

Suppose you look at a coin face on, and then edge on, from the same distance away each time. Obviously the quarter's apparent size will be very different in the two cases. Is that because something happened to the quarter? Did the quarter's atoms shrink? Was there some sort of weird bubble of space in the face-on case that then went away in the edge-on case?

Your questions about length contraction in spacetime are just as outlandish as the ones I just posed for the quarter. What is "really" happening with length contraction is just as mundane and uninteresting as what happens with the quarter when you change the direction from which you look at it.

 

[Orodruin]

Having taught both special and general relativity courses several times in addition to hanging in this forum for 8 years I have concluded that there are some fundamental issues regarding time dilation and length contraction: very few students really understand their meaning. They both have very particular interpretation and it is exceptionally easy for students to forget this, sometimes because teachers and textbooks don’t really emphasize the underlying assumptions but also many times just because the concepts are already ingrained in students’ minds from popular accounts even before starting the course. Both time dilation and length contraction are fundamentally connected to the relativity of simultaneity and it is easy to misapply them — particularly length contraction. This is part of the reason that this year I left out any discussion on length contraction for the last few lectures so that students could get familiar with the rest of the theory first.

Another important thing to remember is that just because one does not understand how something works, it does not mean that it is wrong. This thread is a typical example of drawing false conclusions based on extrapolating the consequences of the theory predictions in an incorrect manner and then concluding that the theory itself must be wrong.

 

[A.T.]

What I mean by real is: does the space between atoms/molecules shrink, do the atoms shrink at the expense of repulsive forces, or is there some sort of magical bubble of spacetime that shrinks as it follows the object undergoing length contraction?

The objects move in 4D space-time such that their projection onto 3D space is smaller. That affects every aspect of the object, like the force-fields between the atoms, so they tend to shrink during acceleration. If you prevent them from shrinking, they will experience actual physical stress and eventually break:
https://en.wikipedia.org/wiki/Bell's_spaceship_paradox

Whether that's "real" for you is your personal preference.

 

[Matt Fenwick]

The objects move in 4D space-time such that their projection onto 3D space is smaller. That affects every aspect of the object, like the force-fields between the atoms, so they tend to shrink during acceleration. If you prevent them from shrinking, they will experience actual physical stress and eventually break:
https://en.wikipedia.org/wiki/Bell's_spaceship_paradox

Whether that's "real" for you is your personal preference.

You get your information from Wikipedia. Lord help you.

 

[weirdoguy]

You get your information from Wikipedia. Lord help you.

No, it's a simple source for you, who has a lot of misunderstandings. Mind you, people who respond here are specialists, there is no need to have that kind of attitude

 

[Matt Fenwick]

Scientists do not get their information from Wikipedia. Length contraction is nothing more than a mathematical construct. It has absolutely no experimental basis in reality.

 

[Dale]

Scientists do not get their information from Wikipedia.

As a professional scientist, I can tell you that this is wrong. I do get some of my information from Wikipedia. I also write information on Wikipedia for others to use. I also quote Wikipedia to people on the internet as an easily accessible resource for them to use, regardless of where I originally got the information.

You are misinformed on multiple points in this thread including the value of Wikipedia, the experimental confirmation of the Lorentz transforms, and the predictions of relativity.

See here for a list of experiments confirming the Lorentz transforms: http://www.edu-observatory.org/physics-faq/Relativity/SR/experiments.html

 

[Ibix]

Scientists do not get their information from Wikipedia.

A fair few of them write it, though. There are some familiar names in the edit history, and it's a decent summary. There is an extensive reference section if you want to read more official sources.

Length contraction is nothing more than a mathematical construct. It has absolutely no experimental basis in reality.

Sigh. Go and look up Purcell's explanation of the force on a moving charge near a current carrying wire. You'll want to buy Purcell's text, of course, since information online can't possibly be right...

 

[Matt Fenwick]

Einstein did not get the Nobel prize for S.R.

 

[Ibix]

Einstein did not get the Nobel prize for S.R.

So what? We don't measure a theory's success by who wrote it or what prizes it's won. We just look at whether it makes accurate predictions.

 

[Dale]

Please get back on topic @Matt Fenwick Neither the discussion of Wikipedia nor the discussion of anyone's Nobel prize is relevant to this thread.

 

[Orodruin]

We just look at whether it makes accurate predictions.

And the myriad of following theories that build upon it that would be fundamentally misguided if it was not correct to high accuracy. In the case of SR, such theories include — among others — quantum electrodynamics which is one of the most (if not the most) numerically accurate theory to date. Arguing that relativity is fundamentally misguided is similar to arguing you can’t build a house with wood and stone.

 

[Matt Fenwick]

No, you are wrong. No one light clock should be any more or less valid than another.

As a professional scientist, I can tell you that this is wrong. I do get some of my information from Wikipedia. I also write information on Wikipedia for others to use. I also quote Wikipedia to people on the internet as an easily accessible resource for them to use, regardless of where I originally got the information.

You are misinformed on multiple points in this thread including the value of Wikipedia, the experimental confirmation of the Lorentz transforms, and the predictions of relativity.

See here for a list of experiments confirming the Lorentz transforms: http://www.edu-observatory.org/physics-faq/Relativity/SR/experiments.html

 

[weirdoguy]

No, you are wrong

You came here to learn, or to argue with those who know way more than you?

 

[Ibix]

No one light clock should be any more or less valid than another.

Indeed. And this claim is incompatible with length contraction not existing - glad to see you starting to come round.