Question about Lorentz contraction

[MortFurd]

Half right. If the ruler tilts, then it will fit through the hole because it's now going through lengthwise. Put a pencil into a soft drink bottle. Put a meter stick through a milk ring. Hard to do crosswise, but easy enough if it's tilted any signficant amount. Nothing do do with decreased foreshortening and everything to do with the angle.



No, it doesn't require that much acceleration.... just enough to miss the far edge of the hole and then go point-first into the gap.

Could you tell me where I messed up, then?
I figure it will take the ruler 1.0167000713642114091967272343367e-9 seconds to cross the hole. That's all the time you've got to deflect the ruler far enough to make it tilt so that the leading edge drops the thickness of the table plus the thickness of the ruler. Figuring that for a 2 mm thick ruler and a 2mm thick table, I got 394,864,606,363,909G of acceleration for a 4mm drop in just 1.0167000713642114091967272343367e-9 seconds. That qualifies as "gargantuan" in my book.



ETA:
I am assuming that we're trying to get the ruler to drop through the hole and not collide with the in side of the hole. If all you want is to pull the ruler far enough down to impact the top edge on the hole, then it would take far less acceleration. As I mentioned above, a 1G field would pull the ruler down by less than the diamter of a hydrogen atom. I don't think you'd get much of a collision out of that, as the surface of the table is going to be far rougher.

 

[jsfisher]

I don't think you're quite understanding his scenario....In particular, it's not physically possible for a 1 ft ruler to fit through a 1/2 ft gap, so if the ruler fit through the gap, the gap must have been larger than the ruler. This appears to be an ojbective (and frame-independent) way to compare two sizes -- but if the size is frame dependent, how can there be a frame-independent comparison?

Right. The posed scenario is that the ruler is traveling across the table at a high relativistic speed (say 0.9999999999c). (An unstated assumption was the presence of a suitable gravitational field.) From the viewpoint of the ruler, the hole in the table is greatly fore-shortened, and at no point is the ruler's center of mass over the hole without both ends still supported by the table. So, a naive conclusion would be the ruler does not drop into the hole.

However, from the table's viewpoint, the speedy ruler is greatly fore-shortened, and as a result spends most of its time traversing the hole with neither end supported. So, it should drop.

The two viewpoints have apparently contradictory final outcomes.

I believe, though, the paradox is resolved by realizing the end of the ruler must bend downward as it starts passing over the gap. So, even from the ruler's vantage point, it still ends up in the hole.

 

[drkitten]

Could you tell me where I messed up, then?


I am assuming that we're trying to get the ruler to drop through the hole and not collide with the in side of the hole. .

Done.

 

[Schneibster]

Of course it's got more energy when it's moving. But it's got more energy whether it's squished lengthwise or from the side, and the additional energy is the constant factor (1-v²/c²)^-1/2, regardless of orientation (as predicted by simple relativistic arguments). And the electrodynamics calculations I did above back that up.

Look, Zig, I basically said, "it's got more energy in the bonds when it's moving at relativistic velocities," and you said, "no, it doesn't." It's really simple, and fifty equations won't get you out of it. Everything gets shorter along the vector of motion, and everything gains energy when it moves, and the laws of physics are correct for all observers. If you want to argue with someone, you have to be prepared to have them say that you said they were wrong, and prove that you were wrong when you said so. I'm sorry you don't like it, but there it is. If you don't like it, don't tell people they're wrong when they say something that's obviously true.

 

[boooeee]

Look, Zig, I basically said, "it's got more energy in the bonds when it's moving at relativistic velocities," and you said, "no, it doesn't." It's really simple, and fifty equations won't get you out of it. Everything gets shorter along the vector of motion, and everything gains energy when it moves, and the laws of physics are correct for all observers.

My bolding. We all agree that a moving object has more energy. But does that mean there is more energy in the bonds?

I read that as saying that it would take more energy to "liberate" a molecule into its constituent atoms if that molecule was moving at a relativitistic speed. Is that a fair summary of your claim?

 

[ponderingturtle]

That's the ultimate goal of his argument, yes.

So as all reference frames are equaly valid, what he would be showing is that either relitivity is logicaly inconsistent, or he is makeing a mistake. That is not a conclusion of relativity but one of the fundamental assumptions.

I don't think it's overly complicated. And I don't think he's trying to "hide" anything; the absolute frame emerges as a consequence of his argument (or would if the argument were valid), not as a premise.

I am saying that his situation is over complex, and in adding in irrelevant details he is trying to confuse people over the details. Unless it is having an acceleration that is measured in c/s^2, then it is not going to be a significant acceleration in the relativistic sense. If there is an acceleration that high, you can't depend on special relativity anyway, you will need general relativity anyway.

As I pointed out, the question "will this object physically fit through this gap" is not does not vary with reference frame. If one observer sees a collision, all will. If one observer sees no collision, none will. The presence or absence of a collision is frame-invariant. The exact details -- for example, the relative scales and timing -- may vary, but at the end of the day, the ruler will be either atop the table or below it, and all observers will agree.

This is true as far as relativity, the problem is that the intent of the construction is to use relativity to make something fit through a gap that it would not classicly fit through. and that is not the way relativity works.

 

[ponderingturtle]

My bolding. We all agree that a moving object has more energy. But does that mean there is more energy in the bonds?

I read that as saying that it would take more energy to "liberate" a molecule into its constituent atoms if that molecule was moving at a relativitistic speed. Is that a fair summary of your claim?

No his claim would seem to indicate that if you burn something traveling at a high speed relative to you, you will see more energy released by the change in chemical bonds than you would otherwise.

 

[drkitten]

So as all reference frames are equaly valid, what he would be showing is that either relitivity is logicaly inconsistent, or he is makeing a mistake.

Well, yes. And both are possible; nothing in science is every proven beyond a doubt. Finding a logical inconsistency in relativity is likely, but not out of the question. That's part of why NSF still funds physics research.

I am saying that his situation is over complex, and in adding in irrelevant details he is trying to confuse people over the details.

And I disagree.

Unless it is having an acceleration that is measured in c/s^2, then it is not going to be a significant acceleration in the relativistic sense. If there is an acceleration that high, you can't depend on special relativity anyway, you will need general relativity anyway.

Absolutely not. The only thing that matters is that the rod's course changed, not the acceleration that it withstood (unless we're talking about materials strength and such like). Prior to reaching the gap, the rod was in an intertial frame. I could just as easily expose the rod to a momentary high-G acceleration to change its line of flight slightly, and then leave it in a slightly different inertial frame... and the question is wheher or not that changed line of flight impacts the table or passes through the gap.

But it's easier to visualize the necessary transverse acceleration if you use gravity to do it instead of a complicated system of high-G servos or something.



This is true as far as relativity, the problem is that the intent of the construction is to use relativity to make something fit through a gap that it would not classicly fit through. and that is not the way relativity works.[/QUOTE]

 

[ponderingturtle]

Absolutely not. The only thing that matters is that the rod's course changed, not the acceleration that it withstood (unless we're talking about materials strength and such like). Prior to reaching the gap, the rod was in an intertial frame. I could just as easily expose the rod to a momentary high-G acceleration to change its line of flight slightly, and then leave it in a slightly different inertial frame... and the question is wheher or not that changed line of flight impacts the table or passes through the gap.

The thing is that you are subjecting it to massive instantaneous velocity changes at relativistic speeds.

So really you need to look at the two sections of the rulers course independently. The first is sliding along the table the second is as it is moving downward.

In neither of these two frames is there a meaningful length contraction in the direction needed for this to work, as it is basically making a right angle turn. And once again if you are bringing in accelerations into this, then from the equivalence principle you need general not special relativity. And then the math gets hard.

But it's easier to visualize the necessary transverse acceleration if you use gravity to do it instead of a complicated system of high-G servos or something.

You are postulating near infinite G servos, billions of G's at least.

This is not a SR problem but a GR problem at it's core. So looking at it with SR is not that helpful.

 

[Ziggurat]

Look, Zig, I basically said, "it's got more energy in the bonds when it's moving at relativistic velocities," and you said, "no, it doesn't." It's really simple, and fifty equations won't get you out of it.

Let's go back to the start. Dr. Trintignant said in the original post:

It's especially curious if one asks what keeps such a moving object in that compressed state. Consider a simple H2 molecule, moving along the bond direction. The two atoms "want" to be a certain distance apart; a distance dictated by electromagnetic and other forces. And yet when moving relativistically, that bond distance appears shorter. It seems to me that even the normally spherical electron orbital of a lone H atom will appear squished into an ellipsoid.
...
Another thing comes to mind--there must be a tremendous amount of energy contained in that distortion. Electromagnetism is a very powerful force. Compressing any solid object along one axis must therefore require an enormous energy input. Is it possible that some--or even all--of the kinetic energy in an object is somehow "contained" in this distortion?

The question had to do with whether or not there was energy in the contraction of the bond length. That question only makes sense in relation to the energy compared to a moving H2 molecule aligned so that the bond length is not contracted. And Dr. T was speculating that there might be an energy difference due to the Lorentz contraction specifically, not just the motion, which would mean that an H2 molecule would have different energy depending upon whether the bond was aligned parallel or perpendicular to its direction of motion.

You responded

I am only guessing, but I'll bet if you worked it out, you'd find that this adds up to the relativistic apparent mass increase.

I responded to you saying,

Well, the energy of an H2 molecule moving at relativistic speeds is just given by E2 = mc2/(1-v2/c2) (using rest mass for m - relativistic mass is redundant with relativistic energy). That doesn't depend upon bond direction, so whether the H2 molecule is aligned along the length of contraction or perpendicular to it doesn't matter.

You replied with

I'd argue that the deformation indicates that the bond is pulling tighter along the direction of motion; pulling tighter requires more energy; and so forth. That was my general line of argument.

Bolding mine.
Now you say

Everything gets shorter along the vector of motion, and everything gains energy when it moves, and the laws of physics are correct for all observers. If you want to argue with someone, you have to be prepared to have them say that you said they were wrong, and prove that you were wrong when you said so. I'm sorry you don't like it, but there it is. If you don't like it, don't tell people they're wrong when they say something that's obviously true.

Yes, everything gets shorter along the direction of motion. Yes, everything gains energy when it moves. But that's not the only claim you made. You claimed that the change in the bond length itself indicated a change in energy (see bolded part above). You objected to my statement that there cannot be any orientational dependence to the energy of a moving hydrogen molecule. But the potentials are no longer isotropic. In fact, I showed that electromagnetic potentials remain constant over the surface of a lorenz-contracted sphere around moving charges. So the lorenz-contracted bond length does NOT indicate a change in energy compared to the only thing relevant to compare it to: a moving bond which is not Lorentz-contracted. The potential energy does increase, but as my calculations show, they increase whether you calculate them along the Lorentz-contracted direction or along the non-Lorentz contracted direction, and by the same amount in both cases (justifying solving the problem with only the relativistic equation for total energy without regard to internal structure). There is NO orientational dependence of the energy of a moving hydrogen molecule, you have provided NO argument beyond vague handwaving for why it should be otherwise, and if it were otherwise then conservation of energy is violated. And your attempts to invoke quantum mechanics and thermodynamic averaging as an escape claus from that violation are simply wrong: a violation of energy conservation is a violation of energy conservation, regardless of how difficult it might be to exploit.

 

[drkitten]

The thing is that you are subjecting it to massive instantaneous velocity changes at relativistic speeds.

Sure. If I can postulate speeds near light-speed, why not?

So really you need to look at the two sections of the rulers course independently. The first is sliding along the table the second is as it is moving downward.

Both of which are inertial frames, and therefore GR is not relevant.

]

In neither of these two frames is there a meaningful length contraction in the direction needed for this to work, as it is basically making a right angle turn.

Absolutely not. All you need is to shift the flight path of the ruler slightly. The ruler is still moving mostly horizontally, so there's still substantial foreshortening in the the direction of travel, which is still mostly colinear with the gap in the table.

And, in fact, the whole point of the argument is specifically NOT to subject the ruler to enough force to make your proposed "right angle turn." Instead, you want to subject it to the smallest possible turn precisely to preserve the maximum amount of lenth contraction..

And once again if you are bringing in accelerations into this, then from the equivalence principle you need general not special relativity.

Er, wrong. You don't need GR.

You are postulating near infinite G servos, billions of G's at least.

It's a thought experiment. I can postulate quadrilions of G's if necessary.

This is not a SR problem but a GR problem at it's core. So looking at it with SR is not that helpful.

I don't know how many times I need to tell you that you're wrong -- but, you're wrong. GR need not enter into it. The ruler can travel in two inertial, one pre-acceleration, another post-acceleration. GR is no more necessary for this problem than it is for the twin paradox; you simply need to accept that at some point an unnamed acceleration did occur.

 

[Ziggurat]

Another earlier quote by you:

What about the strength of the field necessary to account for the closer bond? Fields are energy, and the EM field explicitly is- its exchange particle is the photon, the quantum of energy.

As I already showed, the field is actually WEAKER, even at the Lorentz-contracted position, along the direction of motion than it is in the perpendicular, non-contracted direction. The potential energy works out to be the same in either case.

 

[ponderingturtle]

Sure. If I can postulate speeds near light-speed, why not?

Because you can not have such high gravitational fields with out stepping into the boundaries of GR

Both of which are inertial frames, and therefore GR is not relevant.

And as there is only one of the frames that is involved in the transit of the table, it is the only relevant frame of reference. Which is what I was saying from the beginning. The initial motion of the ruler is irrelevant as that is not how it is moving.

Now with the relativity of simultaneity you will get weird bending in some reference frames as you need to specify which reference frame the whole ruler turns simultaneously and then it will not be a simultaneous change for other reference frames.

But if you are considering gravity and acceleration and not just hand waving changes in reference frame you are going to need GR.

Absolutely not. All you need is to shift the flight path of the ruler slightly. The ruler is still moving mostly horizontally, so there's still substantial foreshortening in the the direction of travel, which is still mostly colinear with the gap in the table.

and that is the point I made you just need to look at the cross sections in the direction of motion after the change in reference frame. The whole thing about their dimensions in the axis of motion is not relevant. So once again you are just making over complicated putting a peg through a hole, and are dealing with it entirely classically.

And, in fact, the whole point of the argument is specifically NOT to subject the ruler to enough force to make your proposed "right angle turn." Instead, you want to subject it to the smallest possible turn precisely to preserve the maximum amount of lenth contraction..

And then you just need to redefine a better coordinate system where the motion is along one axis.

That is the point the goal of this is to add irrelevant complexity to confuse people into thinking that there is something inconsistent with SR. There isn't, now it might not be right, but it is self consistent.

Er, wrong. You don't need GR.

Yes you do, if you want to make it actually accelerating and more complex than just looking at the cross section perpendicular to the direction of motion for the two objects. And that is a purely classical issue there. as you don't get any relativistic effect perpendicular to the axis of motion.

It's a thought experiment. I can postulate quadrilions of G's if necessary.

And you are getting confused by over complicating the situation and not redefining the coordinate system to the obvious convenient one.

I don't know how many times I need to tell you that you're wrong -- but, you're wrong. GR need not enter into it. The ruler can travel in two inertial, one pre-acceleration, another post-acceleration. GR is no more necessary for this problem than it is for the twin paradox; you simply need to accept that at some point an unnamed acceleration did occur.

GR has to enter into it, if you are making it more complicated that putting a peg into a hole. As this is not really any different and you simply have to look at the crossections of the peg and hole perpendicular to the direction of motion, there is nothing that needs relativity about it.

 

[Ziggurat]

Regarding the whole ruler-hole thing, you don't need gravity at all. Use some other force to push the ruler downwards. Put a static electric charge on it, make the table a perfect uncharged insulator, and stick an oppositely charged (but also insulating) surface under it. All you need for the problem is a force, the details of the source are unimportant to the essence of the problem.

 

[Yllanes]

Regarding the whole ruler-hole thing, you don't need gravity at all. Use some other force to push the ruler downwards. Put a static electric charge on it, make the table a perfect uncharged insulator, and stick an oppositely charged (but also insulating) surface under it. All you need for the problem is a force, the details of the source are unimportant to the essence of the problem.

You don't even need a force. The problem (the relevant part) can be posed as follows:

Assume we have a car and a garage of equal proper length. The garage has two doors at both ends, which are open. A man in the garage closes both doors as soon as the back of the car enters the garage. From his point of view the car is Lorentz contracted and fits easily. However, from the point of view of the car the garage is Lorentz contracted and too small to accomodate it. What happens? (Assume that the car either crashes through the front door without slowing down or that the doors are shut and open instantaneously, to avoid unnecessary complications).

 

[Schneibster]

Again, Zig it's perfectly simple: nothing that is moving by at relativistic velocities will be observed to have less energy as a result. You said (and have repeated above) that it will. I say that's dumb, because it ignores the Lorentz-Fitzgerald contraction. You're trying everything you can to squirm out of that. I'm watching with amusement. Feel free to squirm some more.

 

[Ziggurat]

Again, Zig it's perfectly simple: nothing that is moving by at relativistic velocities will be observed to have less energy as a result. You said (and have repeated above) that it will.

I have no idea why you persist in misunderstanding what should be a very simple idea.

Compare: 2 hydrogen atoms at rest and at a distance to 2 hydrogen atoms at rest and bonded. Which has lower energy? The bonded hydrogen atoms.

Compare: 2 hydrogen atoms in motion and at a distance to 2 hydrogen atoms in motion and bonded, Which has lower energy? The bonded hydrogen atoms.

Do you actually disagree with either statement?

Bonding lowers the energy with respect to the non-bound state. That is always true. That's why it's a bound state. It is not their motion which makes them lower energy, because certainly a moving pair of bonded hydrogen atoms is higher energy than a pair of bonded hydrogen atoms at rest. I not only said so repeatedly, I gave the equation for how much more energy they have.

I say that's dumb, because it ignores the Lorentz-Fitzgerald contraction.

You don't need to consider Lorentz contraction to figure out the energy. All you need is the rest mass and the velocity. That was my whole point. But if you actually do the calculations (which I did and you have not disputed) for what the relevant potentials are for moving bonds, you find that the potentials are modified by the same factor, whether you consider the Lorentz-contracted direction or the un-contracted direction. Considering the Lorentz contraction's affects on the bond energy will produce the EXACT SAME ANSWER you get by just using the simple equation E = mc²/(1-v²/c²)^1/2. It just takes more work. And you have provided precisely ZERO evidence that this is in any way wrong.

You're trying everything you can to squirm out of that. I'm watching with amusement. Feel free to squirm some more.

A hydrogen molecule in motion with the bond direction aligned parallel to the direction of motion has the SAME energy as a hydrogen molecule with the bond aligned perpendicular to the direction of motion. That has been my position from the start. Introductory relativity indicates this. Conservation of energy requires it. And electrodynamic calculations back it up. I'm not squirming at all. Quite the reverse: you have provided no evidence beyond handwaving that the bonding energy for a hydrogen molecule in motion should be different if the bond direction is perpendicular rather than parallel to the direction of motion, you have still failed to address the fact that this would violate conservation of energy, and your attempt at finding a loophole for that violation was shot down easily without any response from you.

 

[Schneibster]

I have no idea why you persist in misunderstanding what should be a very simple idea.

Maybe it's because you keep saying the same dumb thing: things that are moving fast will have less energy.

You don't need to consider Lorentz contraction to figure out the energy.

Honestly, you keep saying stuff like this and expect me to respond in any way but to say it's dumb?

 

[69dodge]

Maybe it's because you keep saying the same dumb thing: things that are moving fast will have less energy.

Less energy than what?

Of course, some moving things have less energy than some nonmoving things. It's only reasonable to compare a moving thing with the same thing when it's not moving.

So now the question is, what does "the same" mean? What moving thing ought to be considered the same as a given stationary thing? In particular, if the stationary thing is actually a pair of objects separated by the distance x, does "the same thing, only moving" consist of (1) a pair of objects separated by the distance x as measured in the frame in which they're stationary, or does it consist of (2) a pair of objects separated by the distance x as measured in the frame in which they're moving?

I think the answer is (1). Maybe the difference between you and Ziggurat is that you think the answer is (2)?

I can't quite figure out what you two are arguing about, to be honest.

ETA: I reread a bunch of posts. I have a better idea of what you guys are arguing about. Ziggurat's arguments make much more sense to me.

 

[69dodge]

About the ruler: I mentioned general relativity earlier, but now I think that was probably a red herring.

Yes, the front end will bend into the hole under the force of gravity (and I think the bending also results in a deceleration of the front), but let's assume an "ideal ruler". Much like an ideal string is massless, this ideal ruler is absolutely rigid; it doesn't bend.

But then you change your mind:

The posed scenario is that the ruler is traveling across the table at a high relativistic speed (say 0.9999999999c). (An unstated assumption was the presence of a suitable gravitational field.) From the viewpoint of the ruler, the hole in the table is greatly fore-shortened, and at no point is the ruler's center of mass over the hole without both ends still supported by the table. So, a naive conclusion would be the ruler does not drop into the hole.

However, from the table's viewpoint, the speedy ruler is greatly fore-shortened, and as a result spends most of its time traversing the hole with neither end supported. So, it should drop.

The two viewpoints have apparently contradictory final outcomes.

I believe, though, the paradox is resolved by realizing the end of the ruler must bend downward as it starts passing over the gap. So, even from the ruler's vantage point, it still ends up in the hole.

Yes, I agree. Bending is the key. There's no such thing as a rigid body in relativity. A rigid body is one whose parts all move simultaneously, and there's no such thing as simultaneity in relativity. (Roughly speaking.)

I think I answered that in an earlier post.
To make the answer clear:
The ruler won't drop into the hole, regardless of Lorentz contractions. At the speed of light (and assuming a 1G field,) the ruler will drop less than the diameter of a hydrogen atom while crossing a twelve inch hole. The surface roughness of the table presents hills and valleys that are hundreds if not thousands of times bigger.

Yes, for the particular case of a foot-long ruler. But we can imagine a really long ruler trying to fall through a really long hole in a really long table. Then it will have plenty of time to drop.

If I drop a rod "horizontally," someone zipping past at near the speed of light will see the rod dropping "tilted," with the amount and direction of the tilt being frame-dependent.

How does that solve the puzzle?

The puzzle is that it seems to be frame-dependent whether the ruler drops in the first place, because in one frame the hole is too short to let the ruler drop at all (if the ruler is rigid). If it doesn't drop, you don't get the tilting.

If G is high enough, then the ruler will tilt.

Tilt? Or bend?

If the ruler is rigid, why would it tilt if it passes over a short hole? However strong gravity is, the same gravity is also pulling on the majority of the ruler that's over the solid part of the table, thus preventing it from tilting into the hole.

I could just as easily expose the rod to a momentary high-G acceleration to change its line of flight slightly, and then leave it in a slightly different inertial frame... and the question is wheher or not that changed line of flight impacts the table or passes through the gap.

The thing is that you are subjecting it to massive instantaneous velocity changes at relativistic speeds.

So really you need to look at the two sections of the rulers course independently. The first is sliding along the table the second is as it is moving downward.

Momentary? Instantaneous? Simultaneity is relative.

"The ruler" doesn't have "a" course. Each bit of it has its own course, which doesn't affect the course of any other bit until enough time has passed for light to travel between the two bits.

If in one frame the back of the ruler is over the hole at the same time that the front is, and in another frame the back of the ruler is never over the hole at the same time that the front is, this is just another way of saying that when the front is over the hole it doesn't care whether the back is also over the hole or whether it isn't. The front will move the same way at that moment in either case. The back can't help hold up the front just because the back is "now" over the table. The "message" that it's over the table hasn't yet had time to reach the front.

Now with the relativity of simultaneity you will get weird bending in some reference frames as you need to specify which reference frame the whole ruler turns simultaneously and then it will not be a simultaneous change for other reference frames.

Yes. Bending.

But why would the whole ruler turn simultaneously, in any reference frame? In all reference frames, the front reaches the hole first and gets pulled down a bit by gravity, and some time is required for the back to "find out" about this event.