A virtual pole vaulter in the relativistic barn

[danR]

I have sent approximately the following to a relativity prof at my university. It's summer, so I don't know if he'll read it, or be interested. So here it is for discussion.

Hello,

I wonder if you could tell me if the following experiment would have merit.

To measure actual relativistic contraction with physical rods is impractical. And we wish to parse out any Penrose-Terrell rotation, so we cannot use some kind of imaging. That would be appearance, and not measure.

We construct the classic pole-vaulter in a barn: the 'pole' is a 100 metre length of relativistic electrons. The 'barn' is a 10 metre measuring area. The two 'doors' at either end of our barn are two magnetic or electrostatic gates.

We send our pole (sans vaulter) into the area. At the correctly calculated time, determined by when the 100 metre pole should just fit the 10 metre barn, pulses are sent to the shutters from one source through two equal length cables. Detectors are positioned with each shutter to measure any electrons shunted off. According to theory, if the beam is going at the right velocity, the detectors do not detect any appreciable ends of the pole chopped off by the closed doors of the barn. Telling us that we have indeed placed the thing altogether in the barn.

The pole vaulter seems like a good gendankenexperiment, but I would like the satisfaction of an experimental realization.

 

[bcrowell]

At any particle accelerator where beams are accelerated up to relativistic speeds, they have to take relativity into account when setting up the beam optics. The fact that these accelerators work properly can be interpreted as a test of SR. My guess is that the equivalent of this experiment has already been carried out at dozens of labs around the world, but nobody published it as a test of the pole-vaulter paradox because it wouldn't be considered cutting-edge science -- SR has been experimentally well established since before we were born. The issue would be what is considered "equivalent."

One issue to keep in mind is that in general it is very difficult to cleanly test a single prediction of a theory unless you have an alternative theory that makes a different prediction about only that one thing. Any real theory makes lots and lots of different predictions. If you verify the theory, you haven't verified just one aspect of the theory, you've subjected the whole structure of the theory to a test. The problem is that we don't have a self-consistent theory that makes different predictions than SR about the pole-vaulter paradox, while agreeing with SR on all its other predictions, such as the twin paradox, etc.

 

[pervect]

I have sent approximately the following to a relativity prof at my university. It's summer, so I don't know if he'll read it, or be interested. So here it is for discussion.

Hello,

I wonder if you could tell me if the following experiment would have merit.

To measure actual relativistic contraction with physical rods is impractical. And we wish to parse out any Penrose-Terrell rotation, so we cannot use some kind of imaging. That would be appearance, and not measure.

We construct the classic pole-vaulter in a barn: the 'pole' is a 100 metre length of relativistic electrons. The 'barn' is a 10 metre measuring area. The two 'doors' at either end of our barn are two magnetic or electrostatic gates.

We send our pole (sans vaulter) into the area. At the correctly calculated time, determined by when the 100 metre pole should just fit the 10 metre barn, pulses are sent to the shutters from one source through two equal length cables. Detectors are positioned with each shutter to measure any electrons shunted off. According to theory, if the beam is going at the right velocity, the detectors do not detect any appreciable ends of the pole chopped off by the closed doors of the barn. Telling us that we have indeed placed the thing altogether in the barn.

The pole vaulter seems like a good gendankenexperiment, but I would like the satisfaction of an experimental realization.

What's the operational procedure for constructing a "100 meter length of relativistic elelctrons"?

If you reverse things, and use relativity to calculate the proper length of a 10 meter (lab frame) beam of relativistic electrons, you'll get 100 meters, but that's not an experiment, that's a homework problem.

 

[yuiop]

Consider the atmospheric muon experiment. It was found that the number of muons arriving at ground level was much greater than the Newtonian prediction due to their short half life. The relativistic explanation is that their half life is greatly extended by time dilation. This is the explanation in the rest frame of the the atmosphere but now consider things from the rest frame of the muons. In their rest frame their half life is 1.56 microseconds and time dilation cannot explain why they reach the ground. The explanation in their rest frame is the the Earth's atmosphere is length contracted by a factor of nearly 7 and so they can travel the shorter distance in their short life span.

See http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/muonex.html#c1


It is also worth noting that scientists routinely take length contraction into account for bunch lengths of particles circulating in accelerators, which is analogous to the pole in the barn paradox.

 

[danR]

A few emails with a prof here underscored a circularity in the choice of the 'length' of electron beam to start with.

The spirit of the question should be understood: the classic pole-vaulter is an illustration, not a test. I wondered if it could be inexpensively realized as a test, not an illustration. To say that SR is tested all the time is not something that regular folk (who like a viscerally satisfying bit of 'proof' thrown to them once in a while for their tax-dollars) are able to understand.

Once in a while they appreciate some physics demo by an astronaut with a toy gyroscope, and the like. Saying particle experiments inherently demonstrate SR all the time doesn't really give them something to grab and say, "Hey, that sucker really does shrink somehow after all!"

I have modified the experiment, starting with a 10 metre (we don't need 100 metres) length of cold electrons, measured in the experimental rest frame as definitely 10 metres to everyone's satisfaction, and the accelerating to a 5 metre test-barn.

But now it's going to get messed up with GR (previously, the beam would be accelerated, then chopped up into 10 m lengths), it's going to be very expensive (unless ebay has cheap accelerators on sale), and laypeople will object the length is going to get all 'mashed-up' by accelerating it (and there may be some truth in that, who knows), so the whole thing will have no meaningful outcome to anyone.