# Thread: imo einstein was wrong or conservation of momentum is wrong

1. i have two spinning weights 1 year light apart united by a weightless string, the system makes one revolution in half year

if i want to send a message from weight a to weight b it will take one year to arrive

but i do the following :i measure centrifugal force and when its 0 it will mean the instant message the string has been cut is been sent

it took 0 seconds to arrive or momentum would not be conserved

this means either faster than light info is posible or conservation of momentum is wrong

2.

3. Wow...if only all those scientists who spent years and years studying physics had ever bothered to think about two spinning objects connected by a string. I can't help but wonder why that scenario never occurred to anyone!

4. luxtpm, at what speed does the tension release wave travel along the string?

5. if the cut the string info goes at light speeds both weights will end with same vectors with which cons of momentum wont be acomplished

yeah i wonder why nobody else thought of this obviety but i rather not to wonder dont want to go paranoid

6. @luxtpm:
Would you please write in a manner everyone can understand what you mean?
I didn't manage to figure the meaning of your words out...

7. The problem is that you are assuming starting conditions that already violate the rules of Relativity. You say that the string is weightless, by which I assume you mean massless. But in Relativity, massless objects can only have a velocity of c. Since different parts of the string must have different velocities, it can't be massless.

Neither can the string be perfectly rigid. This means that the string must stretch under the tension of holding the balls in their paths. This tension stores energy. Once you cut the string at the first ball, the energy stored in the string starts to collapse the string. this energy and momentum travels along the string and is transfered to the other ball. IOW, if you take the momentum of the first ball and compare it to the momentum of the second ball + the momentum of the string (including that due to the string snapping back, you will find that it all balances out and momentum is conserved at all times after the string is cut.

If you start with an impossible premise, you will get impossible results.

8. Originally Posted by luxtpm
if the cut the string info goes at light speeds
No it doesn't.

9. Originally Posted by Ophiolite
Originally Posted by luxtpm
if the cut the string info goes at light speeds
No it doesn't.
Yes it does. The forces that the two balls have on eachother via the string would travel down the string at light speed, informing each ball that there is another ball tugging on it. When the string is cut, the information of a lost connection would travel down each side of string at light speed to inform each ball that it wasn't being tugged on anymore.

10. That information would only travel at light speed in some idealized situations. The pressure wave of a real string, being a massive object, wouldn't reach that speed.

11. That's the real scenario though, and I replied to Ophi replying to his situation using a 'massless' string. In that case it would travel at light speeds. Or, a more realistic example (only slightly) assume that we can 'stretch' a proton to be one light year long. With that standard, the mass of the string is negligible to the system and the energy transfer from the cut would travel at nearly light speed, I'd hazard to say so near that our current measuring equipment wouldn't be able to tell the difference, nor the two balls spinning about each other.

I am capable of being wrong though, as I am human and not the most well versed in this field, so if that's not right, by all means correct me.

12. Well, either of those situations would be an idealized situation. If you were to try it with a real string, it'd be slower.

13. Originally Posted by Arcane_Mathematician
That's the real scenario though, and I replied to Ophi replying to his situation using a 'massless' string. In that case it would travel at light speeds. Or, a more realistic example (only slightly) assume that we can 'stretch' a proton to be one light year long. With that standard, the mass of the string is negligible to the system and the energy transfer from the cut would travel at nearly light speed, I'd hazard to say so near that our current measuring equipment wouldn't be able to tell the difference, nor the two balls spinning about each other.

I am capable of being wrong though, as I am human and not the most well versed in this field, so if that's not right, by all means correct me.
In such a situation the impulse travels at the speed of sound for the the medium.

So what is the speed of sound for a proton?

The speed of sound for a medium is found by

Where C is the elastic modulus of the medium and p is the density.

A proton is about 1.7e-15 meters across and has a mass of 1.67e-27 kg which gives it a density of 6.49189e17 kg/m³

Now let's take a stab at the elastic modulus:

It is found by

Stress is the force causing the deformation divided by the area of the cross section it is acting across.

Strain is the relative deformation.

We'll assume that the as the proton is stretched out is merely deforms in a a new shape, which gives us a "string" 1 light year long and with a radius of 2.94194e-31
meters.

Assuming the balls mass 10kg, and are moving at 0.1c we get a centripetal force of 1.9 Newtons, divided by the cross-section of the string gives us a stress of 6.99725e60 N/m²

We will assume that this is the force deforming the proton. (if it is removed, the proton will return to its natural shape.)

The proton is deformed from 1.7e-15 m to 1 ly which gives a strain of 5.56518e30

From this we get an elastic modulus of 1.25733e30 N/m²

Finally, we can find the speed of sound through our proton string, which turns out to be a little under 5% of c.

14. Exactly. I wasn't even considering a string composes of a 'particle', but a more realisitic string. My point was exactly as Janus has said in his opening sentence - the information would be transmitted at the speed of sound inwhatever material the string was composed of. It is by ignoring this fundamental that luxtpm has arrived at his mistaken ideas.

15. what i dont understand is that if the string is 1 light second long and it makes half revolution in one second when the signal cut the string arrives both weights will be going in the same direction

16. The string can't make 1 revolution per second if it's one lightsecond long. That would imply that the end of the string traveled over 3 lightseconds in one second.

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