Math Is Fun Forum

JaneFairfax

Member

Registered: 2007-02-23

Posts: 6,868

Faster than light speed possible?

Let us define the “crossover point” of a pair of scissors as the point at which the blades cross (namely point C in the diagram).

[align=center][/align]
When the scissors are wide open, the crossover point is close to the pivot; as you close the blades, the crossover point moves towards to the tips of the blades until, when the blades are fully closed, it coincides with the blade tips.

Now, here is stunning thought: it is possible for the crossover point to move arbitrarily fast!

Here are my calculations. Let us assume our scissors have parallel-edged blades pivoted at a point midway between the parallel edges of each blade. Suppose each blade has length

(measuring from the pivot to the tip) and width

, and that the angle between the blades is

. Let

be the distance of the crossover point to the pivot.

Then a bit of geometry shows that

. Differentiating with respect to time

gives

, where

. Note that

as

.

is twice the magnitude of the angular velocity of each blade and may safely be regarded as constant. It then follows that as

,

.

Note that if the blades are of finite length,

will never be zero. However the minimum value of

is when the blades are fully closed, when more simple geometry shows that

. Thus, if we allow

to be arbitrarily large, then

can be arbitrarily close to 0, and so

has no upper bound.

Now, does this go against Einstein’s theory of special relativity, which sets the speed of light in a vacuum as the absolute upper limit? The answer is: not at all. Special relativity only applies to physical objects. The crossover point on our scissors is not a physical object and thus is not bound by the laws of special relativity.

http://math.ucr.edu/home/baez/physics/R … ssors.html

luca-deltodesco

Member

Registered: 2006-05-05

Posts: 1,470

Re: Faster than light speed possible?

There are many occurences of things travelling faster than the speed of light; for example the path of a beam of light emitted from a distant fast rotating pulsar.

The difference, is that in none of these occurences of things travelling past c, is any information able to be transmitted.

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The Beginning Of All Things To End.
The End Of All Things To Come.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Faster than light speed possible?

Hi Jane;

According to Raymond Chow, Luca is right, but Gunter Nimtz doesn't agree he believes he has already sent information at over 300 times c using quantum tunneling. Saw a doc on it.

Check the works of Miguel Alcubiere. Space itself has no limit on how fast it can be expanded or contracted, that is the basis of his super luminar travel.

Also as far as I understand and that is not much what Einstein called spooky action at a distance, (one of his attempts to find a contradiction in quantum mechanics) travels faster than c (it is instantaneous, thus the contradiction).

Last edited by bobbym (2009-08-24 14:36:32)

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: Faster than light speed possible?

I think this argument may be abstracted too much.

A similar theory for faster-than-light travel of information uses a very big pole (say, 1 lightyear long).
The theory is that someone at A can push the pole, and then the person at B will see it move, getting information instantly that should have taken a year to be transmitted.

The flaw there is that the ends of the pole don't move together. It's not noticeable on normal-sized poles, but there is always a tiny delay between you moving one end and the other end catching up, while the molecules sort themselves out.

I'd imagine it'd be a similar story for the scissors. For a certain point on the scissors to become a crossover point, it would first have to move. But for it to move, it would need to have received the 'signal' from the other molecules. This signal would move at lightspeed or slower.

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Why did the vector cross the road?
It wanted to be normal.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Faster than light speed possible?

Hi Jane;

I am having a problem working through your idea. It is very possible that I am in error. I am getting the limit ds/dt as θ->0 as  - ∞ rather than ∞. What I am doing wrong? Does that change anything if it is - ∞? Can the rate change of the distance with respect to time be negative?

Last edited by bobbym (2009-08-25 03:35:15)

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

luca-deltodesco

Member

Registered: 2006-05-05

Posts: 1,470

Re: Faster than light speed possible?

bobbym, what you are referring to in your action at a distance is quantum entanglement, which is a perfectly real phenomena, but again, no information can be transferred.

---

The Beginning Of All Things To End.
The End Of All Things To Come.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Faster than light speed possible?

Hi luca-deltodesco;

First, I am not a physicist, so feel free to reject any of this.

I think Everett with his "many world theory" cleared this up. It comes from Einstein, who hated quantum mechanics. He posed this thought experiment as a bust to quantum mechanics. If a particle and its anti-particle were at opposite ends of the universe and I changed the spin or charge of the first particle then instantaneously the other particle would adopt the reverse spin or charge, otherwise the law of conservation of charge and spin are not true. Since Einstein argued that info can't travel faster than light he believed this could not happen.

A lab experiment was done and the change of the second particle was observed, thus destroying Einsteins last attack on quantum mechanics. Saw it on a documentary but can't remember the name of the documentary.

About information, as I said Raymond Chow and Gunter Nimtz are arguing that very point. Since neither had a clear understanding of what the definition of information is they could not agree. (same documentary).

Last edited by bobbym (2009-08-25 04:40:27)

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

luca-deltodesco

Member

Registered: 2006-05-05

Posts: 1,470

Re: Faster than light speed possible?

spin and charge are inherit properties of basic particles, which cannot be changed, only observed. quantum entanglement describes what you are talking about though, if two particles for example are entangled, and you observe one to have a positive spin, then the other particle MUST have a negative spin.

But like i said, information cannot be transferred, because you cannot control what the spin on your particle is when it is observed, all you know is that the other particle must have the opposite.

---

The Beginning Of All Things To End.
The End Of All Things To Come.

JaneFairfax

Member

Registered: 2007-02-23

Posts: 6,868

Re: Faster than light speed possible?

Hi Jane;

I am having a problem working through your idea. It is very possible that I am in error. I am getting the limit ds/dt as θ->0 as  - ∞ rather than ∞. What I am doing wrong? Does that change anything if it is - ∞? Can the rate change of the distance with respect to time be negative?

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Faster than light speed possible?

Hi Jane;

Thanks, I think I see what you are driving at.

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Ricky

Moderator

Registered: 2005-12-04

Posts: 3,791

Re: Faster than light speed possible?

But like i said, information cannot be transferred, because you cannot control what the spin on your particle is when it is observed, all you know is that the other particle must have the opposite.

You're saying it's not information because you can't change it?

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"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

TheDude

Member

Registered: 2007-10-23

Posts: 361

Re: Faster than light speed possible?

I think he's saying that you can't pass information using this method.  For example, let's say you take 2 particles that are entangled and transport them 1 lightyear away from each other.  If a scientist measures the first particle's spin then he immediately knows what the spin of the other particle is, even though it's 1 LY away.

Now, you could say that he gained information on the second particle immediately by measuring the first one, but really the information didn't transfer immediately.  It existed when the particles were first created, it just wasn't measured.  It then took a certain amount of time to transport the particles 1 LY apart, during which time they traveled less than the speed of light, so information traveled slower than the speed of light.

Now, what luca is saying is that you can't change the spin of a particle.  So while you could say that the spin of a particle is information, it cannot be used to send information faster than the speed of light.  It traveled with the particles as they were transported 1 LY apart.

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Wrap it in bacon

Ricky

Moderator

Registered: 2005-12-04

Posts: 3,791

Re: Faster than light speed possible?

It existed when the particles were first created, it just wasn't measured.

This is one of the hardest things to understand (or perhaps, simply become accustomed to) in quantum physics.  The thing is that it didn't exist when the particles were created.  There are several states (spins) a particle can have, and we can express the probability that a certain particle is in a certain state, called the wave-function.  When the state is actually measured, we know with certainty which state the particle is in, and the wave-function is said to "collapse".

All this is perfectly fine, except for one thing.  Scientists currently think (and experiments have given them good reason to) that the wave-function is not just based on our incomplete knowledge, but the "probability aspect" is actually a physical phenomenon.

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"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."