DIY Experiment of Special Relativistic Effects?

[Sciencemaster]

TL;DR Summary

Is there an experiment I could perform to prove the occurrence of relativistic effects to myself without relying too heavily on other assumptions or results, preferably with little to no laboratory equipment?

I'd like to perform an experiment that will build intuition for Special Relativity in the real world. While I do believe that it occurs in the real world, I'd like to be able to prove it for myself, and I feel that such an experiment would help others on this forum as well. Is there an experiment I could perform to prove the occurrence of relativistic effects to myself without relying too heavily on other assumptions or results, preferably with little to no laboratory equipment? For example, Fizeau's light-travelling-in-water experiment (showing the relativistic addition of velocities) could be such an experiment, as it shows that the velocities add in a nonclassical way without relying too much on other measurements. Thank you for any and all help, I appreciate it!

Note: I've been able to detect cosmic ray muons using a single scintillator in an undergraduate laboratory before, but as it was only one device, I couldn't effectively filter cosmic ray muons from other particles unless they decayed, which was not all of the incident particles, and didn't give an accurate measurement of how many had decayed relative to a different amplitude anyway. I would appreciate help creating an experiment that would show these effects directly (and to an extent, accurately).

 

[Rive]

I don't think it can be done properly DIY.

There may be some chances around the GPS system, but while I'm not really familiar with the thing at that level I'm sure it'll require plenty of digging and planning.

For GR, you may get appropriate close-to-Sun star images for a desktop-Eddington from the SOHO Stargazer project. I don't really know if resolution is adequate or not, but maybe worth a shot.
Though this one is also not really DIY, but at least feels doable.

 

[PeroK]

In many ways the basic test of SR is to put a particle in an accelerator and try to accelerate it past the speed of light. Again, hardly DIY, but a simple and conclusive test of SR against Newtonian physics.

 

[topsquark]

It doesn't feel quite like what you are looking for, but you should be able to do the Michelson-Morely experiment. (It will have to be in two experiments, 6 months apart.)

-Dan

 

[sophiecentaur]

I don't think it can be done properly DIY.

I'd agree with you but we could be proved wrong by just one contribution that says "I did it on my kitchen table and the method was as follows". But it would be down to the definition of "DIY".

However, merely demonstrating a magnetic force between conducting wires is, arguably proof of the relative effect on moving charges.

 

[Sciencemaster]

Upon further thought, I believe it is possible to build a DIY Michelson interferometer and then use clear PVC pipes with water flowing through them along one of the arms of said interferometer to create a viable setup for Fizeau's running water experiment. The problem is that the difference between the relativistic case and a nonrelativistic case is roughly n=10^-7 (where I am calling n the difference between c in vacuum and c in the medium, regardless of the source of the change in velocity). Using a green laser of roughly 530 nm in said interferometer (assuming an arm length of half a meter) will produce a difference between the interference pattern of the relativistic case and that of the nonrelativistic case of roughly 1/5 of a fringe. While you could use lenses to magnify this result, I imagine the noise inherent in doing this DIY would make this impossible even with a basic DIY shock absorber. Would there be any way to make it so that you could measure this result? Perhaps a modification to the setup that would reduce noise or make the difference between the cases greater? I'd love to hear peoples' thoughts on this.

 

[Baluncore]

What happens if you switch from water, to a much higher flow velocity of hydrogen gas?

 

[DaveC426913]

This might be a great time to reintroduce Project GREAT from 2005, wherein a family man took his kids in a camper van to the top of Mt. Rainier, along with a bunch of atomic clocks.

http://leapsecond.com/great2005/

OK, this is GR, not SR, but still...

And, technically, three cesium clocks might count as "laboratory equipment". I guess not all you of have a couple in your kitchen junk drawer.

 

[Sciencemaster]

What happens if you switch from water, to a much higher flow velocity of hydrogen gas?

Well in that case, if the gas has a velocity of 924.6 m/s (a reasonable speed I got off stack exchange) and index of refraction of 1.00013881, we get a difference of index of refraction of of roughly 10^-9 if the nonrelativistic case keeps the speed of light in the gas invariant (c/n) (i.e. the flow of the gas does not affect the speed of light through it)--a smaller value because of how small the index of refraction is. However, if the velocities add classically (i.e. u'=u+v), then the difference is roughly 6*10^-6, which is better. This leads to a difference about roughly 10 fringes with the same setup (which could *hopefully* be measured with enough noise reduction). However, it would be better to have a setup that could rule out both cases.

 

[Sciencemaster]

This might be a great time to reintroduce Project GREAT from 2005, wherein a family man took his kids in a camper van to the top of Mt. Rainier, along with a bunch of atomic clocks.

http://leapsecond.com/great2005/
View attachment 337566

OK, this is GR, not SR, but still...

And, technically, three cesium clocks might count as "laboratory equipment". I guess not all you of have a couple in your kitchen junk drawer.

Alright, that is a cool experiment that would definitely fit the criteria, at least for GR. The main problem here is that I don't have any Cesium clocks, and they seem pretty expensive for the average person (myself included)...

 

[DaveC426913]

Perhaps you could go next door and ask your neighbor if he has a cuppa Cesium clocks you could borrow?

 

[sophiecentaur]

Perhaps you could go next door and ask your neighbor if he has a cuppa Cesium clocks you could borrow?

An easier experiment which would be doable in the home could be to use the Mossbauer Effect. This was discovered in 1958 and we actually did it in university labs in about 1965 (so red hot off the press at the time) . Basically you can detect the effect of very low relative velocities or differences in g when an absorber and a gamma emitter are moved (or placed) relative to each other. When the nuclei are bound in a crystal structure (iirc it was steel, the frequency width of the resonance is (in the right materials) narrow enough for the absorber resonance to be offset enough to stop absrption.
If health and safety would permit (in the years since the 60's) then all that's needed is a gm counter and a tall building (they claimed it would work between floors of the lab building) but we just used a very slow moving mount for the absorber and looked for the absorption curve width. Much cheaper than using atomic clocks.

 

[Sciencemaster]

An easier experiment which would be doable in the home could be to use the Mossbauer Effect. This was discovered in 1958 and we actually did it in university labs in about 1965 (so red hot off the press at the time) . Basically you can detect the effect of very low relative velocities or differences in g when an absorber and a gamma emitter are moved (or placed) relative to each other. When the nuclei are bound in a crystal structure (iirc it was steel, the frequency width of the resonance is (in the right materials) narrow enough for the absorber resonance to be offset enough to stop absrption.
If health and safety would permit (in the years since the 60's) then all that's needed is a gm counter and a tall building (they claimed it would work between floors of the lab building) but we just used a very slow moving mount for the absorber and looked for the absorption curve width. Much cheaper than using atomic clocks.

That seems like a good idea. At a glance, I worry that this might be a bit too indirect of a test of SR to build intuition and such, but that might be because I'm not *too* familiar with the effect, and it definitely has potential. I know it shows the difference in the frequency of emitted radiation due to time dilation, but would you mind clarifying how it shows relativistic effects a little bit?
At any rate, is there a good setup for a DIY version of this to test special relativistic time dilation? Specifically, getting the geiger counter to move relative to the source without having its changing distance from the source impacting the result. I'm imagining a rotating platform, but then the effects of rotation (non-inertial reference frame) come into play. Also, what kind of gamma radiation source would one use? I'm imagining Ba-133 or Cs-137 if you can get those DIY.

 

[Vanadium 50]

all that's needed is a gm counter

Um....no.

You need something that can select the energy of the Mossbauer line. An HPGE detector would be my first choice. Also, the velocity variation demonstrates only a classical Doppler shift,

If you want the GR Pound-Rebka experiment, your problem will be source intensity. You need a good signal meters away from your source. Not easy, not cheap, and not possible without an NRC permit.

 

[sophiecentaur]

Um....no.

Well . . . .it's nearly Christmas . The setup in our lab was little more than a slow motion drive and a gm counter. The whole kit sat on a bench top. Even with a lot more trimmings (including the right isotope, of course) it would be a lot more affordable than two Caesium clocks. I do realise that what we were looking at may have been little more than the Doppler Effect and that, to see the effect of GM would involve a much bigger apparatus and a more powerful source - probably out of doors with a fair bit of lead around it.

But what impressed me and stayed with me for decades was the incredibly narrow resonance we were looking at on the 'kitchen table'.

 

[Vanadium 50]

I have a really hard time understanding how this will work with a Geiger counter. A Geiger counter integrates over energies and to a degree particle type (beta or gamma). So you not only see the line you are interested in, you see every other line, plus the lines degraded by Compton scattering, plus the continuum. If you want to use a gas detector (not my first choice) you have to run it in proportional mode, not Geiger mode. Otherwise, your signal is buried in lots of noise.

MIT's junior lab manual for this is online. They use a gas detector, but in proportional mode,

I looked for what was originally used, but everything seems behind a paywall. A few years later, scintillator seems common. Mossbauer was operating at low temperature for other reasons, so if he used a gas detector, it needed to stay gaseous at these temperatures. Probably excludes krypton (a good choice) and maybe even argon.

 

[sophiecentaur]

I have a really hard time understanding how this will work with a Geiger counter. A Geiger counter integrates over energies and to a degree particle type (beta or gamma).

We just counted clicks (mechanical counter, iirc). 'They' wouldn't have told us about any pre-filtering of unwanted products (e.g. Beta) but a suitable screen could have helped with background radiation count (? dunno about such things, myself). Maybe there's a particular isotope that worked best.

It may well have been a great confidence trick on us undergraduates but I doubt that the main principle didn't apply. The absorption dip / with speed change (fractions of a mm/s) was very narrow so it would have been hard to fudge. I threw out my old lab books several decades ago so I have no evidence.

 

[Vanadium 50]

I think it is more likely that you were given a proportional counter and told it was a Geiger counter. They look identical. A "screen" won't help you since the background is coming from the source itself. But every experiment has a trick, and the trick here is to know what you are looking at.

However, my earlier points stand. Pound-Rebka is GR not SR, and requires a long vertical distance and a crazy hot source to cover that distance. Mossbauer by itself just shows a classical Doppler shift. The OP should really try something else.

In principle, the Transverse Doppler Effcet is a good test. It is conceptually not too horrible. Unfortunately, the classic Ives-Stilwell experiment requires some non-trivial skill, and usually a mictospectrograph. An Echelle would probably help. Couple in the high voltage, vacuum, the need to build the apparatus in a vacuum tube and the like and the practicalities kill you.

Getting back to the radio telescopy thread, a great way to do this would be to watch the pulsars overhead. You look at one pulsar as it moves from in front of you to behind you (as the Earth rotates) and your time base is every other pulsar in the sky. You should be able to measure the Earth's rotration speed using SR down to 100 km/hr. Unfortunately, a homemade radio telescope is unlikely to be able to measure hundresd if pulsars. The math is not simple - the fact that the pulsar will not be exactly overhead makes it tricky, but it also turns out this is necessary for the measurement to work.

 

[Vanadium 50]

Three thoughts:

1. Direct measurements of the time required to see relativistic effects is tough. Light travels at a foot per nanosecond, so you need a ~1 GHz scope to put your equipment together. These are easy enough to find, but they are several thousand dollars.

2. GPS is an option, provided using someone else's satellites isn't cheating. You need to do a lot of work, though. The problem is you will need to separate the SR effect from the unknown GR effect. The way you do this is to recognize that on the horizons, the satellite is moving at 18000 mph with respect to you, but overhead it is only moving at 17000 mph (because of the Earth's rotation).

To do this, you will essentially need to build your own GPS decoder - the commercial ones take this effect out (so they can tell where you are), and you need to leave it in. This should work, at least statistically, but I suspect that actually doing this will expose all sorts of issues that need to be understood and addressed.

3, There is a cosmic ray muon experiment you can do without a mountain. But it takes the same sort of equipment as in your college lab. Here is how it works conceptually: I have two detecots, one above the other, serparated by say a foot. Below the lower counter I have an iron stack and a third counter that I can place anywhere in the stack.

If all three counters fire, I know I have a cosmic ray that penetrated the lowest counter. I can measure its initial speed by looking at the time difference between the signals on the top two counters. By varying the depth of the third counter, I vary the minimum energy of cosmic rays I am looking at. Does their speed vary with energy (Newtonian) or not (relativistic). This can be fancied up, and I probably would, but that's the idea.

 

[Sciencemaster]

That variation of the cosmic ray experiment shows promise. Plus, with that configuration, you could also take it to a mountain and measure the difference in events detected as well, giving one two possible SR experiments with one setup. Would it be at all reasonable to get some sort of such particle detector (such as a scintillator or something else) for personal (DIY) use?

 

[Vanadium 50]

Well, there's good news and there's bad news. The good news is that a 10 cm x 10 cm x 1 cm piece of scintillator is a $5 in bulk. A silicon photomultiplier is maybe $40-70, so counters are $100 each or so. Maybe less.

The bad news is that the electronics will cost. You are going to need a discrimInator per channel. a coincidence unit, a time-to-digital converter, and something to analyze the output. Oh, and a power supply for the SiPMs. Oh, and cables - LEMO cables are like $40 each. Most university physics departments have much of this lying around. You probably don't. It's a few thousand if you needed it all new. And while you probably don't need a GHz scope to do the measurement, you probably do to set things up.

It's hard to do anything much simpler, but even this will have a pretty scary price tag all in.

Maybe you could borrow most of it.

Oh. and taking equipment up a mountain is non-trivial. It has to be plugged in somewhere.

 

[sophiecentaur]

Um....no.

You need something that can select the energy of the Mossbauer line. An HPGE detector would be my first choice. Also, the velocity variation demonstrates only a classical Doppler shift,

If you want the GR Pound-Rebka experiment, your problem will be source intensity.

You are the cold light of reason here and I may need to modify my memory of a 1960s demo. I take the point about the GR version and that all we saw was doppler but the GM tube we used was almost certainly the same design as the standard GM tubes I've seen and used subsequently (Nothing like images i see on google). The counter was almost certainly a mechanical type (or Decatron?). So that would mean they chose a very suitable source and absorber just to demonstrate the resonance.

 

[dlgoff]

An easier experiment which would be doable in the home could be to use the Mossbauer Effect. This was discovered in 1958 and we actually did it in university labs in about 1965 ...

Yes. I did that experiment back in the 1970's with Iron that was sent into my Universities nuclear reactor (which was dismantled due to public concern ... Dang public)

 

[sophiecentaur]

Yes. I did that experiment back in the 1970's with Iron

Iron (steel) rings a bell in my memory. I've no idea where they got the source. IT may have been brought over form the Cullham labs specially for our labs but H and S was a much lower priority in those days. We used to clean the mercury in the school prep room as a favour to the lab technician in the early 60s and brew coffee in chemical glassware on a bunsen burner.

 

[Vanadium 50]

TeachSpin's muon lifetime experiment - not what you want exactly, costs $5800. That should set the scale.

CAEN, ij Italy, has a unit that will do everything you want - power, readout, coincidence, send it to a PC. It's about $250.channel. I know they have a 64 channel version. They may have a 16 channel version, which could be more affordable.

You also need - minimum - about 100 pounds of iron in your range stack.

 

[Sciencemaster]

3, There is a cosmic ray muon experiment you can do without a mountain. But it takes the same sort of equipment as in your college lab. Here is how it works conceptually: I have two detecots, one above the other, serparated by say a foot. Below the lower counter I have an iron stack and a third counter that I can place anywhere in the stack.

If all three counters fire, I know I have a cosmic ray that penetrated the lowest counter. I can measure its initial speed by looking at the time difference between the signals on the top two counters. By varying the depth of the third counter, I vary the minimum energy of cosmic rays I am looking at. Does their speed vary with energy (Newtonian) or not (relativistic). This can be fancied up, and I probably would, but that's the idea.

Would you mind explaining why the speed of the particles wouldn't vary with energy in the relativistic case? I imagine it has something to do with a relationship between decay rate and energy causing some particles with lower velocities to decay before reaching the detector in the Newtonian case, while most particles experience enough time dilation that this doesn't really matter in the time before reaching the detector in the relativistic case. I'm really not sure, though, and I would appreciate some insight.

 

[Ibix]

Would you mind explaining why the speed of the particles wouldn't vary with energy in the relativistic case?

It does vary. However, for things traveling near the speed of light you can double the energy while the speed only varies on the 3rd/4th/5th (or more) decimal place. To the precision you can measure, all the muons you see will be doing $c$ (formally, speeds indistinguishable from $c$) and only their energy will vary.

That's not the case in Newtonian physics - to double the energy you need to increase speed 41%, no exceptions, and there's no upper limit. So if you see a range of energies with negligible variation in speed you've falsified Newton, even if you haven't formally verified Einstein.

 

[Vanadium 50]

What @Ibix said.

In Newtonian physics,
$$E = \frac{1}{2}mv^2 + m$$
$$v = \sqrt{2E/m - 1}$$

In Relativity
$$\frac{E}{m} = \frac{1}{\sqrt{1-v^2}}$$
$$v = \sqrt{1-\frac{m^2}{E^2}}$$

Here I am working in units where the speed of light is equal to 1. As described, the apparatus will look at muons with energies from about 200-1000 MeV, and the muon mass is about 100 MeV. So in the Newtonian world the velocities range from about 1.5 to 4.5, and in an Einsteinian world, they ramge fromabout .85 to .99.

Distinguishing .85 fro .99 is hard, as you would need to perform an absolute calibration good to a fraction of a nanosecond. Thta's hard. Instead, we look at velocity vs. energy - does it change by 15% or by a factor of 3?

As Ibix said, you probably can't tell that there has been a 15% change, and to be fair, I didn't design the measurement to do that. But you could certainly tell it isn't 3.

You can probably tell that making it bigger helps. If I make the experiment twice as tall, I get twice the time separation and twice the energy difference, so I get 3x the separation between Newtonian and relativistic. The evil dark side of this is that it works in both directions - make it just a little smaller and you lose a lot of sensitivity.

 

[Sciencemaster]

Alright, thank you for the information! Maybe I’ll see if I can borrow some equipment…

[Mentor Note: Cross-post has been edited out of this post]