Nature of Time Dilation and Length Contraction

[MacM]

Well, at least we can agree on that much. Fortunately my case doesn't hinge on the price of refried beans in Mexico.



No, it's a short paragraph that illustrates the evidence that supports length contraction. I'm sorry that you found it too difficult to read. But it does in fact show that in order for your point of view to be taken seriously it would require that both reason and evidence must be thrown out the window.

Spoken like a true ignoramous. Go to school and try to learn something, Mac.

None of your babble here has anything to do with SR spatial length contraction. Please be specific and make your case that a magnet and coil with a relative velocity somehow suggests, much less proves, contracton.

We are waiting.

[Tom2]

No MacM, we are waiting. We're waiting for the clear logic of my initial argument to sink in to your thick skull.

[Pete]

You might be waiting awhile. For Mac, logic means:

1) Deny A until A is false, and repeat B until B is true.

2) If that doesn't convince them, try again with CAPS for IMPORTANT WORDS.

3) If it still doesn't work, reformulate 1) - repeat "A is Babble" until "A is Babble" is true.

Surprisingly, this last appears to have worked (albeit subjectively), since it seems clear that logical arguments are, in fact, babble in Mac's ears.

[Tom2]

I have no illusions. I know that MacM is never going to understand. It's not going to stop me from pointing out how stupid he is though.

That reminds me...

MacM, I see that you are still squirming instead of justifying your statement about length contraction being "mathematical hogwash". So I feel obliged to say it again:

You're such a weasel. You're constantly pointing it out when people make statements "by fiat". And yet here you are with the tables turned, and rather than support your assertion you ask for a disproof of it.

[MacM]

No MacM, we are waiting. We're waiting for the clear logic of my initial argument to sink in to your thick skull.

Your continued insults in lieu of posting supporting information for your position is most telling.

[MacM]

You might be waiting awhile. For Mac, logic means:

1) Deny A until A is false, and repeat B until B is true.

2) If that doesn't convince them, try again with CAPS for IMPORTANT WORDS.

3) If it still doesn't work, reformulate 1) - repeat "A is Babble" until "A is Babble" is true.

Surprisingly, this last appears to have worked (albeit subjectively), since it seems clear that logical arguments are, in fact, babble in Mac's ears.

See my reply to Tom2 above.

[MacM]

I have no illusions. I know that MacM is never going to understand. It's not going to stop me from pointing out how stupid he is though.

That reminds me...

MacM, I see that you are still squirming instead of justifying your statement about length contraction being "mathematical hogwash". So I feel obliged to say it again:

You're such a weasel. You're constantly pointing it out when people make statements "by fiat". And yet here you are with the tables turned, and rather than support your assertion you ask for a disproof of it.

Considering that you never replied in physics terms to gedankens demonstrating the failure of your pet theory I do not feel inclined to continue to repost the scenario.

Just explain how you propose to justify claiming length contraction when the clock tick rate used to time a trip fully accounts for the accumulated time on the clock without length contraction.

[Tom2]

Your continued insults in lieu of posting supporting information for your position is most telling.

I did post supporting information you idiot. The magnet/loop experiment was one of the experiments that set Einstein, Lorentz, Poincare, Larmor, and the rest of the physics community on the search for the set of transformations that leaves classical electrodynamics invariant under a change of inertial frames. That experiment, as well as any other experiment in electrodynamics, demonstrates that nature respects the symmetry of uniform relative motion.

And as for your "hogwash" comment:

You're such a weasel. You're constantly pointing it out when people make statements "by fiat". And yet here you are with the tables turned, and rather than support your assertion you ask for a disproof of it.

[Pete]

Considering that you never replied in physics terms...

Repeat B until B is true

How many years, Mac?

[Tom2]

Considering that you never replied in physics terms to gedankens demonstrating the failure of your pet theory I do not feel inclined to continue to repost the scenario.

There is no gedanken experiment that can demonstrate the failure of SR. At least, that's what I assume you mean by my "pet theory".

Just explain how you propose to justify claiming length contraction when the clock tick rate used to time a trip fully accounts for the accumulated time on the clock without length contraction.

For the love of god just try to follow my argument. Then you'll have your answer.

[Tom2]

Janus,

I get your post, but I think you're point will be lost on those who need to get it. So I hope you don't mind if I give away the answer.

Mammals give live birth.
Cats give live birth.
Therefore cats are mammals.

This argument is deductively invalid, yet its conclusion is true.

Only birds lay eggs.
Alligators lay eggs.
Therefore Alligators are birds.

This argument is deductively valid, yet its conclusion is false.

The point is that there is no connection between deductive validity of an argument (which is what most people mean by "logical") and the truth or falsity of its conclusion. In fact validity has nothing to do with the truth or falsity of the premises either.

For any true statement P, it is possible to construct an invalid argument whose conclusion is P. And for any false statement P, it is possible to construct a valid argument whose conclusion is P.

[Raphael]

Tom2,

Both arguments are deductively valid, they follow the same form. If the conclusion is contrary to other facts, then one or more of the premises is falsely presented not the method to determine the conclusion.

[Pete]

Mammals give live birth.
Cats give live birth.
Therefore cats are mammals.

All A are B
All C are B
Therefore all C are A

This is not a valid argument.

Compare:

Horses give live birth.
Cats give live birth.
Therefore cats are horses.

The form of the second argument is different, and valid:

Only A are B
All C are B
Therefore all C are A.

[Raphael]

Mammals give live birth.
Cats give live birth.
Therefore cats are mammals.

All A are B
All C are B
Therefore all C are A

This is not a valid argument.

Compare:

Horses give live birth.
Cats give live birth.
Therefore cats are horses.

The form of the second argument is different, and valid:

Only A are B
All C are B
Therefore all C are A.

We will now be debating semantics.
"Mammals give live birth," does not imply that all mammals give live birth. Nor does "cats give live birth" imply that all cats give live birth. The premises were falsely presented, the form of the argument is correct. By implying the existance of the operator you are changing the logical argument.

For the purposes of live birth, cats are horses.


See if this helps:

All mammals give live birth.
All cats give live birth.
All cats are mammals.
My cat will never give live birth.
My cat is not a mammal.

[Pete]

"Mammals give live birth," does not imply that all mammals give live birth.

Fair enough. What does it imply? Some mammals give live birth? That still doesn't make a valid argument.

the form of the argument is correct

Are you seriously suggesting that cats are horses?

[funkstar]

Why would you think you can apply a false premis as a basis for a logical conclusion?

That is totally illogical.

Someone is in serious need a refresher (or possibly a first course) on formal logic.

I can recommend you some books, if you'd like. This is a serious offer, by the way, and I'll extend it to everyone who wants to know more about formal systems and the like...

[Raphael]

Fair enough. What does it imply? Some mammals give live birth? That still doesn't make a valid argument.

A premise of a logical argument need not be precise, in order for the argument to be valid. If the conclusion differs from other known facts, one or more premises were falsely stated.

Are you seriously suggesting that cats are horses?

I am suggesting that when it comes to live birth of mammals, a cat is equivalent to a horse. When decribing a live birth of a cat or a horse, it doesn't matter if you are using the word horse or cat.

[funkstar]

The premises were falsely presented, the form of the argument is correct.

I think that Janus' point was that the argument isn't deductively valid, so the naïve reading is fine. In any case, just take the simplest interpretation possible. In propositional logic this is

Premise: A => B
Premise: C => B
(apply rule "logic dictates")
Conclusion: A => C

which is not a valid deduction, since a model such as {A true, B true, C false} satisfies the premises but not the conclusion. It doesn't matter what A, B and C stand for nor whether they hold in any particular model such as, say, the real world, the argument is still invalid. Or, if you like, the rule "logic dictates" makes the system unsound.

[Raphael]

I think that Janus' point was that the argument isn't deductively valid, so the naïve reading is fine. In any case, just take the simplest interpretation possible. In propositional logic this is

Premise: A => B
Premise: C => B
(apply rule "logic dictates")
Conclusion: A => C

which is not a valid deduction, since a model such as {A true, B true, C false} satisfies the premises but not the conclusion. It doesn't matter what A, B and C stand for nor whether they hold in any particular model such as, say, the real world, the argument is still invalid. Or, if you like, the rule "logic dictates" makes the system unsound.

True enough, but again semantically speaking, we can not imply that B is a consequence of A (and C). B could be a definition of A (and C).

[funkstar]

Your notation is true enough, but again semantically speaking, we can not imply that B is a consequence of A (or C). B could be a definition of A (or C).

A, B and C have no implicit meaning. A => B and C => B are assumed as premises in the argument. Whether or not they are true in any particular model is irrelevant. And by exhibiting just one model where the premises hold and the conclusion does not, I have demonstrated that argument must be incorrect.

[EDIT:] Technical note - The argument could actually be perfectly valid within the rules of the system. That wouldn't be natural deduction, though, which is what is implicitly meant by "logic" by most people (even if they don't know it.) Furthermore, if the system were unsound, a counterexample wouldn't even prove the argument wrong.