Lorentz Contraction ?s and Implication

[PAllen]

(I did the calculation in my head - if I'm way off some other reader will correct me, but it's a big explosion in any case)

A cute rule to know that I've checked very carefully, is that for gamma factor k, each gram of matter has KE equivalent to 20 kilotons (= 1 Nagasaki atom bomb) per k. So for gamma of 5, that is 100 kilotons TNT per gram. Perhaps 1 kg (which would leag to 100 megatons) is a bit heavier than the average meter stick.

 

[Nugatory]

A cute rule to know that I've checked very carefully, is that for gamma factor k, each gram of matter has KE equivalent to 20 kilotons (= 1 Nagasaki atom bomb). So for gamma of 5, that is 100 kilotons TNT per gram. Perhaps 1 kg (which would lead to 100 megatons) is a bit heavier than the average meter stick.

I assumed 1KG for the mass of the meter stick - a bit heavy as you say, but easy to calculate with because I also selected the gamma factor of 5 to make it easy to work with 1MT=5x10¹⁵ Joules (easy to remember after you've said it fast a few times - "5-10-15").

But I think I should have chosen gamma=6 because the rest mass of the meter stick is rather broadly redistributed but doesn't convert to energy?

 

[Apophenia]

See the digression below, but to answer the question I think you're trying to ask...
If it were not a muon coming down at relativistic velocities, but instead some macroscopic object, then yes, it would appear contracted to the earth-bound observer.

Of course no one has any experience with macroscopic objects moving at relativistic velocities. An ordinary meter stick moving at a speed sufficient to produce a five-fold contraction would hit the Earth like a 100 megaton hydrogen bomb (I did the calculation in my head - if I'm way off some other reader will correct me, but it's a big explosion in any case) and flatten every building and tree for tens of miles around. This is why we don't/can't do direct length contraction experiments with macroscopic objects.

(Digression: You are typing too quickly, as your question has the same logical structure as "Would the earth-bound observer also potentially see X if seeing X were somehow possible?", and the answer to that is clearly, tautologically, and unhelpfully "yes" for just about any X no matter how absurd.)

...helpful to me. I just want to distinguish what constitutes observers and such. For example, anything not within the frame of the muon is contracted as observed from the muon and visa versa.

Yes, the question was completely hypothetical.
Thanks.

 

[PAllen]

I assumed 1KG for the mass of the meter stick - a bit heavy as you say, but easy to calculate with because I also selected the gamma factor of 5 to make it easy to work with 1MT=5x10¹⁵ Joules (easy to remember after you've said it fast a few times - "5-10-15").

But I think I should have chosen gamma=6 because the rest mass of the meter stick is rather broadly redistributed but doesn't convert to energy?

Well, the 100 megatons is pure KE, so it will go somewhere if the meter stick hits the earth. It's really hard to find data from experiments that could answer details on questions like this. There was thread here a while ago speculating on what happens if a base ball 'appears' at the pitcher's mound going at .99c towards home plate? The consensus was that it would release only about 1% of its KE (still a lot) by home plate. But try looking for information about the mean free path of nitrogen nucleii in material similar to a baseball, at .99c. Relativistic ion colliders use neither baseball targets nor nitrogen ions.

 

[Dale]

I understand completely why the issue may not matter to the macroscopic result but am intently curious and think any scientist should be.

Scientists should be curious, but they also need to be logical. Part of being logical is making sure to use well defined terms. Being curious doesn't justify being sloppy in your thinking.

 

[Dale]

The mindless constituents of the muon seemingly "know" they are traveling at a speed v and the dimensions of atmospheric space ahead of them should contract.

Huh?!? How on Earth do you get that idea? That is one of the strangest statements I have ever seen.

 

[ghwellsjr]

Would the Earth bound observer also potentially see the muon with contracted dimensions if somehow possible?

The main thing that particularly bothers me (take the muon traveling through atmosphere case):
Again I may just be looking at it the wrong way but these are how I see the possibilities of what it infers with LC:

The mindless constituents of the muon seemingly "know" they are traveling at a speed v and the dimensions of atmospheric space ahead of them should contract.

I just want to distinguish what constitutes observers and such. For example, anything not within the frame of the muon is contracted as observed from the muon and visa versa.

Did you study the link I provided for you in your other ongoing thread covering muons?

Here is at thread that deals with the tradeoff between Length Contraction and Time Dilation for an incoming muon.

 

[nitsuj]

Huh?!? How on Earth do you get that idea? That is one of the strangest statements I have ever seen.

"The mindless constituents of the muon seemingly "know" they are traveling at a speed v and the dimensions of atmospheric space ahead of them should contract."

I think it was to add integrity to his/her following statement, how the process must be mechanical. A deduction of sorts I guess.

however without knowing what "Length Contraction is "mechanical"" means it's...

But a false premise though, of course motion is relative, in turn the muons..."mechanically" are traveling near c, which is "mechanically" equivalent to being at rest. In comparison to a lesser speed though, i.e. observation of contraction/dilation there is a difference. But that's due to the comparative motion between the observer and the muons.

 

[Naty1]

Apophena:
do recall that right now YOU appear to be moving at near light-speed in many,many observers frames of reference. So they THINK your clock is running really,really, slow compared with theirs. Of course I know 'better', I am sitting here stationary so I know what's 'real'...
[note to police: That is a joke!]

 

[danR]

I hope the intervening discussion has not lost your original question(s):

Wiki quote: "In physics, length contraction – according to Hendrik Lorentz – is the physical phenomenon of a decrease in length detected by an observer of objects that travel at any non-zero velocity relative to that observer."

According to Lorentz himself, yes, that's how he thought of it: the 'actual', 'spacial' 'whatever' gap between the constituent molecules decreased 'physically' in length. Even from the 'moving' object's measurement point of view. That is not the shortly later interpretation of the Lorentz contraction.​

I read the first statement in wiki and already have questions. Now it says "detected by an observer of the object". Is this saying it is merely an observer effect, i.e., the object only contracts apparent to the observer who is seeing it with relative velocity; the object relative to itself does not contract?

Yes. That is the post-Lorentzian interpretation of Lorentz contraction.​

If in fact Lorentz contraction states that an object actually shortens:
Is the general explanation that space is the introduced substance that contracts with the implication that the object shortens without changing it's internal material characteristics (other than space if that is considered an intrinsic property of matter)?

As shown above 'Lorentz contraction' has two different interpretations. It is universally accepted that Lorentz' interpretation was wrong, so the conditional fails.​

And actually, to add to your headache, an actual 'observation', in terms of say, taking a pico-second photograph of an object speeding by at .9 c, there would be an 4D geometric 'rotation' illusion showing in your photograph. This is the Penrose-Terrell-(some other people I forgot) rotation. You can find youTube animations simulating this illusion. The result is that spheres (including the spherical distribution of nucleons in a gold nucleus) would not actually appear flattened. If you decompose a sphere into an assembly of rods, all pointing in the direction of travel, each rod would appear to have rotated frontmost toward the observer such that the leading forward-nether tips of the rods would come into view, and the trailing backward-near tips would disappear from sight.

The sphere itself would not seem flatten, but each constituent rod would seem 'shorter', but only by reason of the rotation.

(A math student—at my university actually—did a math project for her undergraduate degree and came to the conclusion, putting everything together, that it is not actually possible to 'measure' Lorentz contraction by any direct observer method. I tried to get in touch with her to see what her prof thought of this, or if she changed her mind; but with no response.)

 

[Apophenia]

Apophena:
do recall that right now YOU appear to be moving at near light-speed in many,many observers frames of reference. So they THINK your clock is running really,really, slow compared with theirs. Of course I know 'better', I am sitting here stationary so I know what's 'real'...
[note to police: That is a joke!]

Yes, I move at near light speed in the frame of a 'light particle'. I should ask him for the answers?
[note to police: That is a joke of a joke!]
Im not that misconceived...but perhaps.

 

[Mentz114]

Apophena:
do recall that right now YOU appear to be moving at near light-speed in many,many observers frames of reference. So they THINK your clock is running really,really, slow compared with theirs. Of course I know 'better', I am sitting here stationary so I know what's 'real'...
[note to police: That is a joke!]

Copyright violation ! I coined the phrase 'relativity police' in 2007. You owe me 0.001c in royalties (cheques accepted).

 

[Apophenia]

Did you study the link I provided for you in your other ongoing thread covering muons?

Yes, I found your post helpful in explaining what LC and GTD infer for the muon but not really in a mechanistic sense which I wish to explain it although it seems to not be explainable in that manner.

ghwellsjr:
They are both in both frames but it's only one of them that is required to explain why the muons reach the ground. But remember, in each object's rest frame, it is only the other moving object(s) that are time dilated or length contracted.

So in the Earth's rest frame, the muons are both length contracted along the direction of motion and time dilated. However, we don't care about the fact that the muons are compressed instead of symmetrically round (or whatever shape they are in in their own rest frame). We only care that time for them takes longer.

And in the muons' rest frame, the Earth and the distance to the Earth is compressed while the clocks on Earth are running slow but the muons don't care about the clocks, they only care that they can survive long enough for the Earth to fly up to them because it is much closer than we say it is.

Thanks

 

[Apophenia]

Copyright violation ! I coined the phrase 'relativity police' in 2007. You owe me 0.001c in royalties (cheques accepted).

cheques -> I had to look that up...shows how much we like to make our own English here.

 

[ghwellsjr]

Did you study the link I provided for you in your other ongoing thread covering muons?

Yes, I found your post helpful in explaining what LC and GTD infer for the muon but not really in a mechanistic sense which I wish to explain it although it seems to not be explainable in that manner.

ghwellsjr:
They are both in both frames but it's only one of them that is required to explain why the muons reach the ground. But remember, in each object's rest frame, it is only the other moving object(s) that are time dilated or length contracted.

So in the Earth's rest frame, the muons are both length contracted along the direction of motion and time dilated. However, we don't care about the fact that the muons are compressed instead of symmetrically round (or whatever shape they are in in their own rest frame). We only care that time for them takes longer.

And in the muons' rest frame, the Earth and the distance to the Earth is compressed while the clocks on Earth are running slow but the muons don't care about the clocks, they only care that they can survive long enough for the Earth to fly up to them because it is much closer than we say it is.

Thanks

Good, I'm glad it helped.

However, what I presented was pure Special Relativity--no General--the Time Dilation had nothing to do with gravity or General Relativity. The Time Dilation caused by gravity effects is not measurable with incoming muons. In fact, the Time Dilation caused by speed is only a very, very coarse measurement since we are looking at a statistical effect related to the half life of millions of muons. We never know for any particular muon how long it is going to last. Even without relativistic effects, there is some non-zero chance that any give muon could make it all the way to the ground. If you wanted to see the gravitational Time Dilation effects with radioactive substances, you would have to take a lot of measurements and even then, your result would be statistical in nature. It's not really a good idea to use radioactive substances to demonstrate Time Dilation caused by gravity. You need very precise stable clocks to do that,

 

[Naty1]

Quote by Naty1

do recall that right now YOU appear to be moving at near light-speed in many,many observers frames of reference.

Yes, I move at near light speed in the frame of a 'light particle'.

no, there is no such observer.

Instead, consider an observer in a fardistant galaxy looking your way...such an observer DOES observe you as moving near light speed.

 

[Apophenia]

Quote by Naty1
Instead, consider an observer in a fardistant galaxy looking your way...such an observer DOES observe you as moving near light speed.

Please explain that a little more.
If we just assume both galaxies lie in a straight path then we use:

s = v+u / [1+(vu/c^2)]

Can you try to explain in relation to the above equation and defining v, u , and s.