## Lorentz contraction

 Quote by JesseM You can't "prove false" a condition that must be satisfied in order for an equation to work. You might as well say "if we plug time-intervals into the length contraction equation rather than lengths, then the equation gives a wrong answer, therefore I've proven that the length contraction equation is false in some circumstances". Well, obviously no you haven't, because one of the conditions of the length contraction equation is that the values you plug in for L and L' must be lengths measured in the rest frame and the moving frame. Similarly, it's one of the conditions of the length contraction equation that L and L' must both be measured during a time period when the object is rigid and moving inertially. If I measured the rest length L of John when he's a baby, and the moving length L' of John when he's an adult, the two lengths won't be related by gamma, but that doesn't prove the length contraction equation false because I didn't satisfy the condition that the object being measured was rigid throughout the period when both measurements were taken.
I am going to prove something false.

The method is called Reductio ad absurdum.

It is a common misconception that you cannot prove something false.

There exists a greatest integer.
I am going to prove this false.

Let n be the greatest integer.

Add 1 to n.

n + 1 > n.

This is an Archimedes argument.

Quote by Al68
What makes no sense? I was just pointing out that most SR scenarios typically stipulate a rod that is rigid, with a "at rest" length that doesn't change because of acceleration. A normal (rigid) rod with a rest length of d would have a rest length of d after any acceleration, and a length of d/gamma in any inertial reference frame.
 Quote by cfrogue This thread has proved this is false.
No it hasn't. It's just shown that you are free to stipulate a (non typical) rod that is not rigid and can have an increasing rest length (stretch). That does not prove that all rods will automatically increase their rest length. That's just absurd.

You purposely stipulated a rod that was stretchy instead of rigid, and that increased its rest length for some unstated reason.

You can't then apply that result to a different situation in which a rigid rod is stipulated.

Are you under the false impression that acceleration causes a rigid rod to increase its rest length? That's the only thing I can think of that would explain your bizarre posts.

Recognitions:
 Quote by cfrogue I am going to prove something false. The method is called Reductio ad absurdum. It is a common misconception that you cannot prove something false. There exists a greatest integer. I am going to prove this false. Let n be the greatest integer. Add 1 to n. n + 1 > n. Contradiction. This is an Archimedes argument.
What the hell are you blabbering about cfrogue? I didn't say you couldn't prove anything false. I said you couldn't prove the length contraction equation false using a scenario in which you violate one of the conditions that are required in order for the the length contraction equation to apply. If you want mathematical analogies, here's one--

Define the "Law of real inverses" to say: for any nonzero real number R, the number has an real inverse 1/R such that R times its inverse 1/R equals 1.

cfrogue-style argument: but look, zero doesn't have a real inverse! Therefore the "Law of real inverses" is false!

Can you see why this argument would be pretty stupid?

 Quote by cfrogue I am going to prove something false. The method is called Reductio ad absurdum. It is a common misconception that you cannot prove something false. There exists a greatest integer. I am going to prove this false. Let n be the greatest integer. Add 1 to n. n + 1 > n. Contradiction. This is an Archimedes argument.
This is not a valid mathematical argument. You are trying to prove that the statement "there exists a greatest integer" is false by demonstrating that, given any integer, you can produce one that is greater by adding 1 to it. However if there were a greatest integer you would be unable to add 1 to it to make a greater one. You are assuming result before you have proved it.

Matheinste.

 Quote by JesseM What the hell are you blabbering about cfrogue? I didn't say you couldn't prove anything false. I said you couldn't prove the length contraction equation false using a scenario in which you violate one of the conditions that are required in order for the the length contraction equation to apply. If you want mathematical analogies, here's one-- Define the "Law of real inverses" to say: for any nonzero real number R, the number has an real inverse 1/R such that R times its inverse 1/R equals 1. cfrogue-style argument: but look, zero doesn't have a real inverse! Therefore the "Law of real inverses" is false! Can you see why this argument would be pretty stupid?
You are getting frustrated.

You are applying universal generalizations you know do not apply.

 Quote by matheinste This is not a valid mathematical argument. You are trying to prove that the statement "there exists a greatest integer" is false by demonstrating that, given any integer, you can produce one that is greater by adding 1 to it. However if there were a greatest integer you would be unable to add 1 to it to make a greater one. You are assuming result before you have proved it. Matheinste.
I suggest you look at the original Archimedes proof.

It is clear to me you do not know how to argue by Reductio ad absurdum.

I do this all the time.

 Quote by matheinste This is not a valid mathematical argument. You are trying to prove that the statement "there exists a greatest integer" is false by demonstrating that, given any integer, you can produce one that is greater by adding 1 to it. However if there were a greatest integer you would be unable to add 1 to it to make a greater one. You are assuming result before you have proved it. Matheinste.
I suggest you look at the original Archimedes proof.

It is clear to me you do not know how to argue by Reductio ad absurdum.

I do this all the time.

The properties of the Integers is that if n belongs to the integers then n + 1 belongs to the integers.

This is Peano arithmetic.

 Quote by cfrogue I suggest you look at the original Archimedes proof. It is clear to me you do not know how to argue by Reductio ad absurdum. I do this all the time.
I have.

That there is no greatest integer is true. It is called the Archimedean property of numbers.

It does not use this "proof".

You are absolutely categorically wrong in your proof. It is a common mistake that many people make and is completely compatible with many of your arguments.

You may get away with wordplay and ambiguityy with verbal atguments in relativity but you cannot get away with it in mathematics.

Matheinste.

Recognitions:
 Quote by cfrogue You are getting frustrated.
Yes, frustrated by the stupidity of your arguments.
 Quote by cfrogue You are applying universal generalizations you know do not apply.
No idea what you mean by "universal generalizations". Here was my analogy again:

 Define the "Law of real inverses" to say: for any nonzero real number R, the number has an real inverse 1/R such that R times its inverse 1/R equals 1. cfrogue-style argument: but look, zero doesn't have a real inverse! Therefore the "Law of real inverses" is false!
Tell me whether you agree or disagree that this is a stupid argument. Now, here's why it's analogous to the length contraction example:

 Define the "law of length contraction" to say: if an object's length is measured in two different inertial frames, and the object is rigid and moving inertially throughout the period that both measurements are made, and if one of the frames sees the object to be at rest while the other frame sees it to be moving at speed v, then Lmoving = Lrest * sqrt(1 - v^2/c^2). cfrogue: but look, if the two measurements are made in a period of time where the object isn't rigid and isn't moving inertially throughout, then it's not true that Lmoving = Lrest * sqrt(1 - v^2/c^2)! Therefore the "law of length contraction" is false!
So if the first argument is stupid, this second argument must be equally stupid, for exactly the same reason.

 Quote by matheinste I have. That there is no greatest integer is true. It is called the Archimedean property of numbers. It does not use this "proof". You are absolutely categorically wrong in your proof. It is a common mistake that many people make and is completely compatible with many of your arguments. You may get away with wordplay and ambiguityy with verbal atguments in relativity but you cannot get away with it in mathematics. Matheinste.
Silly.

Prove it is wrong.

 Quote by cfrogue Silly. Prove it is wrong.
I cannot be bothered.

I have learnt from experience that if you have decided you are correct, no amount of logical argument will convince you otherwise. However in this case there is no doubt, your proff is invalid.

Matheinste

 Quote by matheinste I cannot be bothered. I have learnt from experience that if you have decided you are correct, no amount of logical argument will convince you otherwise. However in this case there is no doubt, your proff is invalid. Matheinste
No problem.

I cannot show you Reductio ad absurdum.

 Quote by cfrogue No problem. I cannot show you Reductio ad absurdum.
That's quite obvious as you do not understand correctly it yourself.

Matheinste.

 Quote by matheinste That's quite obvious as you do not understand correctly it yourself. Matheinste.
If you want, I can show you some math arguments of mine if you could follow them.

Yea I know, you understand everything.

 Quote by cfrogue If you want, I can show you some math arguments of mine if you could follow them.
That's very kind of you but I have plenty of textbooks and the mathematicians on the math forum are very helpful, and rigorous. Perhaps you should let them look at your above proof and comment on it.

Matheinste.

 Mentor It appears unlikely that this thread will make any substantive progress, so it is now closed.