Pole-barn paradox, one question

[FIL]

[mentors’ note: moved from another thread because it’s a different question]
Preface: I'm an idiot who occasionally watches science videos and has questions.

If it's not inappropriate to tag on to this post, as I too have questions regarding relative simultaneity and apparent contradictions, I'd like to explore the ladder and barn thought experiment a bit.

This stems from watching a Don Lincoln video about the barn paradox where a ladder larger than the barn can fit into it because of length contraction and the simultaneity of the doors, etc. I think I actually understand everything he said while explaining it but wondered about a situation in which the doors activated a mechanism.

Knowing that the barn observer can see the ladder fully fit into the barn and close both doors while the ladder is inside, what happens if we have a high powered laser suspended from the barn ceiling that is turned on when both doors are shut simultaneously. I know it can't be instant but if each door shot a photon at the laser when the door closes, and the laser only switches on when it gets hit by two photons at the same time wouldn't we have a scorched ladder for the barn observer and a pristine ladder for the ladder observer?

Thanks, and like I said I'm an idiot so be nice lol.

 

[FIL]

Thanks for moving my comment, sorry about that

[Mentor replies “no problem, no apology needed”]

 

[Dale]

if each door shot a photon at the laser when the door closes, and the laser only switches on when it gets hit by two photons at the same time wouldn't we have a scorched ladder for the barn observer and a pristine ladder for the ladder observer?

Actually, you would get a scorched ladder for both observers. You already specified what happens for the barn observer.

For the ladder observer the back door closes first and sends a photon towards the laser. But the laser is moving away, so the distance the photon must travel is larger than half the ladder and takes a long time. Then later the front door closes and sends a photon towards the laser. The laser is moving towards, so the distance is shorter and takes less time. The photons wind up both reaching the laser at the same time, turning on the laser and scorching the ladder

 

[FIL]

Actually, you would get a scorched ladder for both observers. You already specified what happens for the barn observer.

For the ladder observer the back door closes first and sends a photon towards the laser. But the laser is moving away, so the distance the photon must travel is larger than half the ladder and takes a long time. Then later the front door closes and sends a photon towards the laser. The laser is moving towards, so the distance is shorter and takes less time. The photons wind up both reaching the laser at the same time, turning on the laser and scorching the ladder

Hey thanks, just to be clear if the ladder is moving from left to right, the back door is the first door it encounters?

 

[FIL]

Ohh nevermind it's the right most door. I think I got it now

 

[Dale]

Hey thanks, just to be clear if the ladder is moving from left to right, the back door is the first door it encounters?

If the ladder is moving left to right then the back door is the right door. I was describing a ladder going in the front door and out the back door of the garage.

 

[FIL]

If the ladder is moving left to right then the back door is the right door. I was describing a ladder going in the front door and out the back door of the garage.

Okay sorry one follow up question. If the ladder is 90ft and barn is 30ft long, the ladder frame sees the barn as contracted right? And the photon from the left door can't be sent until it closes. So wouldn't that result in only like the last 5ft of the ladder getting scorched, but perhaps more for barn observer?

 

[Dale]

If you work it out you will always get the exact same fraction of the ladder is scorched. You can add more complications, it just makes the analysis more complicated.

 

[FIL]

Yeah that makes sense. There's a lot to keep track of when you first learn about this stuff. Thanks for your time

 

[PeroK]

Yeah that makes sense. There's a lot to keep track of when you first learn about this stuff. Thanks for your time

This is why you need a systematic way to describe the coordinates of events in one frame and transform them to another frame. This takes the sting out of these so-called paradoxes. Once you understand how to apply the Lorentz Transformation, it all becomes rather straightforward!

 

[L Drago]

This is why you need a systematic way to describe the coordinates of events in one frame and transform them to another frame. This takes the sting out of these so-called paradoxes. Once you understand how to apply the Lorentz Transformation, it all becomes rather straightforward!

According to lorentz length contraction. Suppose the barn is at rest with respect to the ground and the ladder is moving in incredibly high speeds the ladder will appear to contract and fit in the barn.

Contracted length = Actual length x power root of 1 - (v²/c²).

From the ladder's perspective the barn appears contracted and it does not fit in the barn. Kindly give your valuable insights about this perspective and formula and clarify if any misunderstanding is there.

 

[PeroK]

According to lorentz length contraction. Suppose the barn is at rest with respect to the ground and the ladder is moving in incredibly high speeds the ladder will appear to contract and fit in the barn.

Contracted length = Actual length x power root of 1 - (v²/c²).

From the ladder's perspective the barn appears contracted and it does not fit in the barn. Kindly give your valuable insights about this perspective and formula and clarify if any misunderstanding is there.

If you have two objects moving at relativistic speed relative to each other, then the question of whether one fits inside the other is frame dependent. Note that "fits inside the other" requires the notion of simultaneity in terms of where both ends of each object are at a given moment (moment = time coordinate). So, it all boils down to the relativity of simultaneity.

Try watching this (and look out for the clocks):

 

[L Drago]

If you have two objects moving at relativistic speed relative to each other, then the question of whether one fits inside the other is frame dependent. Note that "fits inside the other" requires the notion of simultaneity in terms of where both ends of each object are at a given moment (moment = time coordinate). So, it all boils down to the relativity of simultaneity.

Try watching this (and look out for the clocks):

Relativity of simultaneity means that two events need not be the same in two frames of reference.

Is this brief description of relativity of simultaneity correct.

 

[PeroK]

Relativity of simultaneity means that two events need not be the same in two frames of reference.

Is this brief description of relativity of simultaneity correct.

It means that if two events have the same time coordinate in one frame of reference, they may not have the same time coordinate in another frame of reference.

Newton assumed a universal time and never considered this possibility.

 

[L Drago]

It means that if two events have the same time coordinate in one frame of reference, they may not have the same time coordinate in another frame of reference.

Newton assumed a universal time and never considered this possibility.

Einstein relativity corrected the gaps in Newton's theory like Newton believed that Time is same in speed in all planets. But Einstein GR model defied it. Newton's theory also had flaws like they could not predict the orbit of Mercury which Einstein's equation correctly predicted.

Einstein special relativity says all inertial motion is relative and kindly correct me if this statement is not true.

 

[jbriggs444]

Einstein relativity corrected the gaps in Newton's theory like Newton believed that Time is same in speed in all planets.

Not just the same speed (progressing at the same rate). The idea that Newton and pretty much all human beings shared is the idea that if we take a snapshot of the universe at an instant in time, that we will all agree about about what things happened at that instant.

For instance, if two flashbulbs go off the standard idea is that there is universal agreement about whether they went off at the same time or not. And if one of them goes off first, that there is universal agreement about which bulb went off first.

That is a statement about absolute simultaneity.

But yes, there is also the idea that every stop watch that is started at one (shared and universally agreed upon) instant and stopped at some future (shared and universally agreed upon) instant will record an identical elapsed time.

That is a statement about an absolute rate at which time passes.

[There is a philosophical point that can be made. It is conceivable that all clocks and physical processes might slow down between two instants. Or speed up. If this were to occur, we would never notice it. Any such effect would be completely undetectible. The philosophical point is that if no experiment can ever detect it, we can safely wave our hands and say that it never happened. No experiment will contradict us]

But Einstein GR model defied it.

Special relativity makes the claim that both above notions about time are incorrect. One does not need general relativity for that.

Newton's theory also had flaws like they could not predict the orbit of Mercury which Einstein's equation correctly predicted.

The Bertozzi experiment is a more direct demonstration that Newtonian mechanics is wildly incorrect for speeds approaching c. It is well worth watching. I think you've been referred to it before.

It is worth watching a second and a third time for all the little bits of useful information and historical perspective that it provides. Using slide rules. Oscilloscopes. Choosing helpful units on graphs. Experimental design and sanity checking. Comparing prediction against experiment. What a linear accelerator looks like. What a vacuum pump (with a reed valve, I think) sounds like. Coax cables and tee connectors. It is a well designed experiment.

Einstein special relativity says all inertial motion is relative and kindly correct me if this statement is not true.

Yes, that is correct. However, it was not Einstein.

Galileo Galilei proposed the principle and Newton adopted it. The result is Galilean relativity or the principle of Galilean invariance. Newtonian mechanics is based on a framework of Galilean invariance.

A problem with Galilean invariance is compatibility with Maxwell's equations for electromagnetism. Light is observed to travel at the same speed for every observer regardless of the emitter. Newtonian mechanics would call for either a universal rest frame for light (a luminiferous ether and a wave propagation model) or a fixed light speed relative to the emitter (a projectile model).

Einstein generalized Galilean relativity in a way that allowed for the experimentally observed invariant light speed relative to any observer along with an identical invariant speed relative to the emitter. This made Maxwell's equations compatible with Einstein's new special relativity.

 

[PeroK]

The Bertozzi experiment is a more direct demonstration that Newtonian mechanics is wildly incorrect for speeds approaching c. It is well worth watching. I think you've been referred to it before.

It is worth watching a second and a third time for all the little bits of useful information and historical perspective that it provides. Using slide rules. Oscilloscopes. Choosing helpful units on graphs. Experimental design and sanity checking. Comparing prediction against experiment. What a linear accelerator looks like. What a vacuum pump (with a reed valve, I think) sounds like. Coax cables and tee connectors. It is a well designed experiment.

Absolutely wonderful and inspiring. Thanks for posting that.

 

[Herman Trivilino]

Newton's theory also had flaws like they could not predict the orbit of Mercury which Einstein's equation correctly predicted.

That is really old and is largely of historical significance only. Since then more modern experiments have not only shown it to be correct, they have solidified it wih more precise and more convincing measurements.

I urge you to read some of the stuff that Clifford M. Will has written. Radar-ranging of Venus, for example, reveals no doubt that Einstein got it right.