A Paradox

[Qfwfq]

Take two large masses far from other large ones, just to make things simpler. Fix them to each end of a rigid rod with a device for measuring attractive force between the two. Make sure the axis a running through both centres of mass has a stable direction, referred to the fixed stars, let things settle nicely and then measure the attractive force, f. Knowing the two masses and the distance r between them, f should match up the well known calculation, proportional to both masses for given r.

 

Now, surely there are many things wizzing along at velocities approaching c and in various directions. From these frames of reference the pair of masses will be wizzing at that velocity, the opposite way. For some directions, r will be contracted, while it won't for directions at right angles to a. For such observers, what should the attractive force between the two masses be?

 

Think carefully... ;)

[FREYA021]

hehehe, look in books for atomic phisics... or IR spectroscopy... harmonic and unharmonic oscilators... if that is elastic or not bond... blablabla

sorry but its done ages ago!

[bumab]

Hmmm....

 

won't the masses appear to change in proportion to the change in r, thus making no difference?

[Qfwfq]

won't the masses appear to change in proportion to the change in r, thus making no difference?

Think so? Try working that out. ;)

[Bo]

as lomg as the observers aren't accelerating, they length contraction etc. is constant, so the system is in equilibrium and they measure a net force of 0 i suppose.

 

Bo

[Qfwfq]

I'm not sure what you mean by a net force of 0, are you sure you followed the description right? It isn't quite so simple.

 

Of course, I did mean inertial observers!

[Qfwfq]

Obviously, there will be equal and opposite forces between the parts and the system will be in equilibrium. For clarity, by "the attractive force between the two masses" we can understand the compressive strain on the rod.

[jartsa]

Let's consider how drilling holes in the walls of a relativistic space ship happens. (astronaut in the ship does the drilling, for the astronaut the walls seem to be homogeneous )

 

Now we observe the drilling from a still standing observer's frame:

Some walls are Lorentz-contracted, some are not.

Energy used to make a hole should be always the same, therefore thin walls must be harder than thick walls. (Lorentz -contracted walls are "Lorentz-hardened")

 

 

So answer to the original question is:

When contraction is 10%, there is 10% hardening on the system, so 10% increase in attractive force.

[LaurieAG]

Hi Qfwfg,

 

Now, surely there are many things wizzing along at velocities approaching c and in various directions. From these frames of reference the pair of masses will be wizzing at that velocity, the opposite way. For some directions, r will be contracted, while it won't for directions at right angles to a. For such observers, what should the attractive force between the two masses be?

 

If you were looking at things from a navigation/mapping perspective and didn't correct for the relative velocities you probably would get a paradox. If you took your navigational queues from an external higher level mapping system you would probably get the correct answer.

[Don Blazys]

For such observers, what should the attractive force between the two masses be?

 

The same...

 

Relativistic considerations also apply to the workings of all measuring instruments and devices.

 

Thus, if the gauge on the rod shows "3g",

then each and every observer will agree,

that "3g" is indeed what they see... see?

Otherwise, they would all be...

relatively krayzee! Just like Don Blazys! :D

 

Don.

[jartsa]

I see we were supposed to use Newton's gravity law G*m1*m2/r^2

That gives a large force increase when r is moderately Lorent's-contracted.

 

Then maybe we should use Coulomb's law on the rod.

That also gives a large force increase when rod is moderately Lorent's-contracted.

 

So the thing stays nicely balanced even when I'm wizzing this way and that way, while watching it.

[jartsa]

Let me try to ask a question.

 

Space ship is traveling at speed 0.9 c. One room of space ship has lights on, the lamp is located at the middle of the ceiling.

Now how much light does the Lorentz-contracted wall receive?

 

(the room is rectangular at rest)

[jakuta]

Take two large masses far from other large ones, just to make things simpler. Fix them to each end of a rigid rod with a device for measuring attractive force between the two. Make sure the axis a running through both centres of mass has a stable direction, referred to the fixed stars, let things settle nicely and then measure the attractive force, f. Knowing the two masses and the distance r between them, f should match up the well known calculation, proportional to both masses for given r.

 

Now, surely there are many things wizzing along at velocities approaching c and in various directions. From these frames of reference the pair of masses will be wizzing at that velocity, the opposite way. For some directions, r will be contracted, while it won't for directions at right angles to a. For such observers, what should the attractive force between the two masses be?

 

Think carefully... ;)

 

This does not bother special relativity unless one wants an absolute answer.

 

Each frame maintains its rules as per the relativity postulate.

 

For example, these masses may be clocks. Each frame will have an interpretation of the time on the clock and this is still consistent witn SR.

[jakuta]

Let me try to ask a question.

 

Space ship is traveling at speed 0.9 c. One room of space ship has lights on, the lamp is located at the middle of the ceiling.

Now how much light does the Lorentz-contracted wall receive?

 

(the room is rectangular at rest)

 

The frame that is moving and "walls" receives no additional light from the view of rest frame.

 

Depending on the direction of motion, say in the direction of travel, the rest observer will simply claim the moving observer will see the light at a time of a lesser value.

[Don Blazys]

Quoting jartsa:

Let me try to ask a question. Space ship is traveling at speed 0.9 c. One room of space ship has lights on, the lamp is located at the middle of the ceiling.Now how much light does the Lorentz-contracted wall receive?(the room is rectangular at rest)

 

From their frame of reference, the on-board, rapidly moving "astronauts" will observe that

the front and back walls are recieving the same amount of light.

 

But from their frame of reference, the stationary "ground crew" will observe that

the back wall is recieving more light,

(because it is approaching the source, and is thus closer),

and that the front wall is recieving less light,

(because it is moving away from the source).

 

However, from any frame of reference (and thus for all observers), the total measured amount of light will be the same.

(Just as for all observers, the total measured amount of attractive force will be the same).

 

In other words, all observers will agree that they are looking at a "100 Watt light bulb" and a "3g" "giant dumbell" !

 

Don.

[jartsa]

I must disagree that a 100 W light bulb is a 100 W light bulb at 0.9 c speed.

It's a 229 W light bulb. (Relativistic Change Factor is 2.29 at speed 0.9 c)

 

Well thinking a bit more, a 100 W light bulb is a 100 W light bulb at 0.9 c speed.

Photons have 2.29 times the energy, and photons are produced at 2.29 times slower rate.

 

 

 

Now I'll use relativity postulate where it's not usually used:

We glue into a stick a measuring stick. Now the length of the stick can be read from the

measuring stick, and the length never changes, so there's never need to talk about "relativistic

length contraction".

 

But "length contraction" is used in relativity, so why not use any silly thing I happen to invent,

like "Lorentz hardening"?

[Qfwfq]

Let me try to ask a question.

 

Space ship is traveling at speed 0.9 c. One room of space ship has lights on, the lamp is located at the middle of the ceiling.

Now how much light does the Lorentz-contracted wall receive?

One may quite easily argue that all the observers should agree upon the number of photons received by each wall...

 

Think carefully folks, it's too easy to say that if everything is done properly things must match up. What is the force for observers with different speeds and at different angles to the rod?