This paradox seems to contradict relativity because in one frame of reference the bug is squashed and in the other frame of reference don't. What do you think?
http://hyperphysics.phy-astr.gsu.edu/hbase/Relativ/bugrivet.html#c1

The "paradox" shows the problems of using special relativity in a situation where acceleration must occur (as the rivet is stopped). I think the real problem here has to do with the rigidity of the rivet.

How? Are you saying that after the head of the rivet hits the wall, the the rivet's end expands to squash the bug? Curious, considering that the rivet has to expand to a size larger than its size at rest. Does it also apply if the rivet is made of a very rigid material, like iron, etc?

Originally posted by Lucas
How? Are you saying that after the head of the rivet hits the wall, the the rivet's end expands to squash the bug? Curious, considering that the rivet has to expand to a size larger than its size at rest. Does it also apply if the rivet is made of a very rigid material, like iron, etc?

Consider this. What happens when the head og the rivet hits the wall? It stops, right? But does the end of the rivet also stop? , No.

The reason being that even for the most rigid object you can think about, the fastest that the information that the head of the rivet stopped can reach the end of the rivet is at the speed of light. Thus the end of the rivet keeps moving unitl it is "informed" that the head stopped. By the time the info catches up, the end of the rivet has squashed the bug. (IOW, the speed of light limit also sets a limit on how rigid a substance can be.)

Some interesting ad-hoc extensions of thought experiment conditions in an effort to support Relativity. (Rigidity or Acceleration). But I don't feel they can be justified. We clearly aren't asking a practical question where someother affect may or may not apply. We are asking a point blank theoretical question about Relativity in its own mathematical constraints.

In that case it appears to fail.

The efforts to be pragmatic and involve issues other than Relavistic mathematics one could state that at that velocity the energy release evaporates the entire local area and clearly the bug is dead. But that goes beyond the question at hand.

I only regret that Einstein never responded to this question. I would love to know his solution.

What about the information in the string I posted "Can You See the Lorentz-Fitzgerald Contraction?"


The very basis of the question appears to be invalid in the first instance in that we may have been taught incorrectly. Length may be viewed as not being purely contracted but rotated via Penrose-Terrell Rotation.

Originally posted by MacM
Some interesting ad-hoc extensions of thought experiment conditions in an effort to support Relativity. (Rigidity or Acceleration). But I don't feel they can be justified. We clearly aren't asking a practical question where someother affect may or may not apply. We are asking a point blank theoretical question about Relativity in its own mathematical constraints.


Janus58 was answering the question from the mathematics of SR. There are no "ad-hoc extensions" here. The relativity of simultaneity can be used to derive the result.

Tom2,

Let me suggest you read the discussion on the link. Simultaneity DOES NOT resolve the issue.

Further people should consider that this type of paradox does not occur in LR.

Originally posted by MacM

Further people should consider that this type of paradox does not occur in LR.

what is LR?

Lethe,

Lorentz Relativity, which actually preceeded SR. It also generates relavistic principles.

This reminds me to another paradox my genious friend once told me:
Two space ships, of the same size (length in this matter), move in a different direction but not on the same line (so one would pass by the other) with a very high speed. One of the ship is armed with laser guns on both of its edges, and is aimed towards the 'line' on which the other ship is travelling. When the two are exactly facing each other, the armed ship fire the laser to the other. Assuming that the two are close enough when they are facing each other, would the unarmed ship get hit?
Maybe a picture may help.

Anyone?

Originally posted by MacM
Lethe,

Lorentz Relativity, which actually preceeded SR. It also generates relavistic principles.

so Mac, is lorentz s aether theory the theory you believe is correct?

Lethe,

so Mac, is lorentz s aether theory the theory you believe is correct?

The data and testing for aether has been less than conclusive. (But not entirely missing).

I think aether must be considerd and greater research aimed at resolving the issue vs simply taking the Einstien/Miller verbal battle results and discarding or distorting the data that was actually found.

Miller gathered data that clearly suggests some form of aether.

I guess my position is "if the shoe fits wear it" but nobody has tried on the shoe since Einstein.

In any case I think this paradox deserves top billing and clearly suggests that Relativity is either wrong or has been extrapolated into areas and "extent" beyond its true nature.

MacM,

If I'm correct, then Lorentz Relativity assumes length contraction without time dilation.

If you're to accept such an unusual psuedo-physical phenomena as length contraction, why are you reluctant to accept time dilation?

I personally don't accept either. :)

Prosoothus,

The following is a response received when posting the "Bug and Rivet Paradox" on MetaResearch.


In LR, no paradoxes are possible because neither time nor space ever changes, and all frames agree about which frame is preferred and which has motion. The clock-slowing effect only works one-way, so that the moving clock slows and the clock in the local gravity field does not. Finally, LR has no length contraction, if my analysis in the latest Meta Research Bulletin is correct.- Tom.


ANS: I personally favor LR even though it hasn't been pursued in enough detail, since Einstien buried it in its enfancy, to be sure it is totally correct itself.

In general it seems to supply all the relavistic functions we need without causing the paradoxes of SR.

MacM,

As far as I know, based on the results of the Michelson-Morley experiment, Lorentz assumed that the reason that the two beams of light in the MM apparatus arrived at their target at the same time was because the length of the arm that was parallel with the motion of the apparatus, through the aether, contracted. If you assume Lorentz's theory to be true, then that would mean that the speed of light is not constant, and therefore implies that there must be an aether.

Later on, Einstein assumed that not only did the two beams of light arrive at their target at the same time in the MM experiment, but that the speed of light remained constant for both beams. In order to explain how this is possible, Einstein added time dilation to Lorentz's length contraction.

To summarize, length contraction is a requirement in Lorentz Relativity, while length contraction AND time dilation are requirements in Special Relativity.

Prosoothus,

I agree with what you have said and I am "Inclined" to believe that there is something that should be called an aether. But its properties are not what was initially thought.

I believe relativity is defining what is caused by such an ether. But that the mis-interpretation of the MMX data and the disregarding of Millers follow on work in that area (which suggest rather strongly there is an aether) and the adaption of a purely mathematical model, where there is no cause for affect, has led us astray and to assume things in Relativity that are not physical reality.

I'm sure this clears everything up.:D

Originally posted by MacM
Some interesting ad-hoc extensions of thought experiment conditions in an effort to support Relativity. (Rigidity or Acceleration). But I don't feel they can be justified. We clearly aren't asking a practical question where someother affect may or may not apply. We are asking a point blank theoretical question about Relativity in its own mathematical constraints.Simultaneity is right there with length contraction and time dilation in SR. I think rigidity was used in the discussion because the effect of simultaneity in this case allows the end of the rivet to continue its motion "after" the head has hit. This is a fundamentally different kind of rigidity than that associated with steady-state stress and strain.

errandir,

Simultaneity is right there with length contraction and time dilation in SR. I think rigidity was used in the discussion because the effect of simultaneity in this case allows the end of the rivet to continue its motion "after" the head has hit. This is a fundamentally different kind of rigidity than that associated with steady-state stress and strain.

I agree with what you say but please note that the link had gone through that scenareo and stated that simultaneity doesn't resolve the issue.

MacM:

Please post the description of the bug-rivet problem as Lorentzian relativity would solve it.

I assume you know how to show that LR does not lead to the paradox, since you seem so confident that the paradox does not arise in LR.

You've made the claim. Now support it with actual explanation.

Thanks.

James R.,

Please post the description of the bug-rivet problem as Lorentzian relativity would solve it.

I assume you know how to show that LR does not lead to the paradox, since you seem so confident that the paradox does not arise in LR.

You've made the claim. Now support it with actual explanation.

Thanks.

ANS: Nice try but let me suggest two things:

1 - Read my post to Prosoothus. I am quoting another source. If that source is wrong then state your case don't expect to slip out of the paradox by issuing a mathematical challenge to me.

2 - Lets not let the issue slip through the cracks by attacking LR but lets see your complete and correct mathematical solution for the paradox which is presented in SR.

Thanks.

That is since you are confident that SR has the solution. We are all intersted.

Originally posted by curioucity
When the two are exactly facing each other, the armed ship fire the laser to the other. Assuming that the two are close enough when they are facing each other, would the unarmed ship get hit?

Yes. An analogous question I’ve asked myself is, If a ship explodes when it is going so fast that it observes galaxy A at the front of the ship and galaxy B at the rear of the ship (closer together due to relativistic length contraction), what do observers in the galaxies see? Galaxy B sees only the rear of the ship explode in its neighborhood. Perhaps a million years later from either galactic observer’s perspective, galaxy A sees the remainder of the ship explode in its neighborhood. What the ship observes happening simultaneously within the whole ship, either galactic observer sees happen in the rear of the ship first. I leave it to you to apply this solution to your paradox.

zanket
Not to annoy you but I'm terrible at deep theories. But I'd like to relate your answer to the problem asked by the thread, and I assume that you would agree that the bug would be squished to death. What do you say?

OK, I have drawn up a *.bmp file to illustrate the resolution to the paradox using the simple simultaneity argument of SR. I didn't use the exact same numbers as the cited webpage, but the idea is the same.

I used:

- v = c/2 => β = 0.5 and γ = 2/√3
- the length of the rivot, as seen by the bug, is 37 pixels
- the depth of the hole, as seen by the bug, is 50 pixels
- the lorentz contraction gives both the length of the rivot and the depth of the hole, as seen by the rivot, are both 43 pixels

This was calculated backwards for the condition that the rivot is travelling just fast enough to squish the bug. The diagram shows the situation from the bugs perspective. I thought that this perspective would be the most instructive, since it demonstrates the scewed now-line of the rivot.

The red coordinate system is the bug's. Notice that the axes are ortogonal. The left verticl red line is the world-line of the edge of the hole. The right verticle red line is the world-line of the bottom of the hole. The horizontal red line is the now-line in this coordinate system when the head of the rivot makes contact with the edge of the hole.

The blue coordinate system is the rivot's. Notice that the axes are scewed. There are three lines, one less steep than the other two (don't let the optical illusion fool you). The left-most steep blue line is the world-line of the head of the rivot. The right-most steep blue line is the world-line of the business-end of the rivot. The shallow blue line is the now line in this coordinate system when the head of the rivot makes contact with the edge of the hole.

The white lines are the light-cone.

I have madet the blue world-lines into dashed lines when they become unphysical. Notice that the world-line of the business-end of the rivot intersects the world-line of the bug just at the point that the situation becomes non-inertial (yellow dot). So, in the context of SR, there is no paradox.

I made the file a gif. I'm assuming those are easier to get a hold of.

errandir,

Interesting. I have two comments or questions.

1 - I wonder why the link (which is strongly relativistic) states simultaneity didn't resolve the paradox. I should imagine you can't answer for them unless as I suspect may be the case it involves point #2 below.

2 - Does the choice of hole depth, rivet length and speed create the specific conditions of a paradox? Since you have used different data, what I am asking is does the specific case as presented also get resolved via simultaneity in your opinion?

Originally posted by MacM
Does the choice of hole depth, rivet length and speed create the specific conditions of a paradox? Since you have used different data, what I am asking is does the specific case as presented also get resolved via simultaneity in your opinion? This is a very fair question, I agree. It does seem just a little scheissty that I used my own numbers, but, I hope that you agree that the paradox is resolved for the numbers I used. I used them because they provided enough symmetry to make the bitmap easy to draw. Were you able to view it? Was it clear?

I really don't want to go through it again, but, if you are interested, just change one of the three values in my example slightly, and see what happens. If you run into confusion, then I'll look into it.

Oh yeah, one more thing. The space-time graph that I drew doesn't really show the paradox, it explicitly shows the resolution. In order to appreciate the paradox, you have to transform to the rivot's frame.

errandir,

Oh yeah, one more thing. The space-time graph that I drew doesn't really show the paradox, it explicitly shows the resolution. In order to appreciate the paradox, you have to transform to the rivot's frame.

I agree. And yes the diagram was clear. Since the link (an they are those that also know and understand SR) states that simultaniety doesn't resolve the paradox, it was and is my belief that your puzzle simply used numbers wherein the paradox doesn't exists so in that regard it may not have resolved anything.

I'm not being negative but pragmatic on that point. It was nice clean work in either case.

To highlite my point assume the hole was 1 cm deep and the rivet is 50 cm long. It is not hard to visulize that for most any speeds of the rivet the bug is squashed. So I do believe one must use the numbers given or simular numbers where the paradox appears.

Originally posted by MacM
... assume the hole was 1 cm deep and the rivet is 50 cm long.In this case, the rivot would have to be moving very fast to realize an ostensible paradox. Assuming it is moving so fast, then the bug will see it as too short, but the rivot will see the hole even shallower than before. In the context of a space-time diagram, just imagine the blue verticle lines sloping shallower to just about parallel with the light cone (almost speed c). Also, you have to steepen the now line in the same manner. Then, look what happens to the point of intersections. The worldline of the rivot end hits the bug before it gets to the nowline of the rivot head hitting the hole edge. So, again, we have dead bug. I'm assuming that, in order to completely satiate you, I will have to crunch the exact numbers from the link.

errandir,

So, again, we have dead bug. I'm assuming that, in order to completely satiate you, I will have to crunch the exact numbers from the link.

My satiation is not your responsibility. :D But I do think since they say your solution doesn't work when it appears to do so, the question can only apply to the specific conditions they have proposed.

Well, it didn't really take as long as I thought to draw up the bitmap. I just had to draw it out on graph paper first. Just to check their calculations:

L_rivot = 0.8 cm
L_hole = 1.0 cm
v = 0.9c
γ = 10/√19 ~ 2.294
L_rivot' = 0.08√19 cm ~ 0.3487 cm

Notice that this calculation ignores specific events in the space-time.

I have again drawn up a bitmap in the bugs rest frame. The origin is the event of contact between the rivot head and the hole edge. The darker lines are the now lines. The brighter lines are the worldlines. Notice that the worldline of the rivot end intersects the worldline of the bug below that now line of the rivot head that passes through the origin. So, the conclusion is that the rivot end hits the bug <i>before</i> the rivot head hits the hole edge. Big portions of these lines are non-physical, and would require a deeper treatment of relativity (and this time I have not perforated those portions). However, for the regions of interest, the lines are valid.

I have indicated the event of the rivot head hitting the hole edge with a dark yellow dot. I have indicated the event of the rivot end squashing the bug with a bright yellow dot. I have indicated the intersection of the worldline of the rivot end with the now line that passes through the origin (a non-physical intersection) with a dark yellow dot. This is to emphasise that the event of bug squash occurs below the now line that passes through the origin.





Oh hell! I just reread the link, and the origin is chosen at the event of the rivot end entering the hole. Do I really have to revise this again? Let me spoil the story be giving away the end: simultaneity wins.

Apparently, I'm also misspelling "rivet."

errandir,

Oh hell! I just reread the link, and the origin is chosen at the event of the rivot end entering the hole. Do I really have to revise this again? Let me spoil the story be giving away the end: simultaneity wins.

:D So your conclusion is that the bug gets squashed from ALL observers view and not just one ?

Hows has the link missed the simultaneity calculation since they specifically mention it?

Originally posted by MacM
So your conclusion is that the bug gets squashed from ALL observers view and not just one ?Yep.




Originally posted by MacM
Hows has the link missed the simultaneity calculation since they specifically mention it? In order to resolve the "swirl paradox" in the "theory of mixing colours," or MC, we have to address the "sufficient-time-to-mix issue."

The paradox goes like this:

We have a gallon of yellow paint in a bucket. Then we dump a gallon of blue paint in the bucket to turn the paint green. We stir it all around for one minute.

MC tells us that yellow and blue make green, and our mixture does this after one minute. But, half a minute after we put the two colours together we don't have green, just a swirl of yellow and blue.

Now we need to use the "sufficient-time-to-mix issue." It takes one minute to sufficiently mix one gallon of each colour of paint. So half a gallon of each colour of paint should be sufficiently mixed in half a minute. But we clearly see that the paint is not sufficiently mixed.

So MC is wrong.

It's a shame that the inventor of MC avoided addressing this paradox.

Notice I showed that yellow and blue don't make green while mentioning the "sufficient-time-to-mix issue."

Originally posted by Lucas
This paradox seems to contradict relativity because in one frame of reference the bug is squashed and in the other frame of reference don't. What do you think?
http://hyperphysics.phy-astr.gsu.edu/hbase/Relativ/bugrivet.html#c1

I don't actually think it contradicts relativity. The theory of relativity suggests that frames of reference can be transformed from one to another through something like the Lorentz transformation.

What this means is that there is a relationship between any frame of reference.

From what I see of the "paradox" (and I do not see a paradox at all) is that all the observers are right, but only from their reference point.

So the bug, the rivet and you the observer are all OK :D

The question could be this, does the bug get squashed. Well it depends on the real length of the rivet when it slows down in terms of the bugs frame of reference. It will suddenly see (assuming that is can 'see' at the speed of light) the extending of the rivet before its squashed (or not).

Anyway check out this site for further information. Thought it was interesting :D

http://www.geocities.com/rumski_mumski/index.htm

Originally posted by curioucity
zanket
Not to annoy you but I'm terrible at deep theories. But I'd like to relate your answer to the problem asked by the thread, and I assume that you would agree that the bug would be squished to death. What do you say?

The bug survives. Recall what I said above, which generalizes to: Given 2 ships moving in opposite directions, what ship A observes happening simultaneously within ship A, ship B observes happen in the rear of ship A first. And vice versa.

Substitute the bug’s home and the rivet for the ships. From the rivet’s perspective, the bug’s home is stopped by the rivet head. If the rivet observes any part of the bug’s home to stop, then it’s a foregone conclusion that the rearward part of the bug’s home already stopped. As it stops it uncontracts. The bug’s home uncontracts ahead of the rivet to keep the bug out of harm’s way.

throw me an aspirin....

curioucity,

throw me an aspirin....

:D