Jump to content

Lorentz-contraction


Recommended Posts

Winterlong;

Let's define the props for this scene. Refer to the U frame.

U is the reference object (a space station) where the anaut A is launched in a ship and follows a circular course while accelerating to a target speed of .6c, then shutting down the propulsion unit. The ship is now moving at constant speed in the x direction as it passes U. There is a static object M (green) .60 distant from U in the x direction.

At U (the origin), A sends a light signal (blue) to measure the distance to M.

The inverse of gamma for v=.6 is .8. The red line indicates an interval of .80 on the U clock is stretched (dilated) to cover the time line of A.

If A assumes he is moving then he should pass M at .60/.6=1.00, yet his clock reads .80. If his clock and his speed are correct, then the distance has changed.

If he assumes a pseudo rest frame, as in the A frame, then M arrives early and the distance has changed.

In SR, the motion of an object does not alter the dimensions of distant parts of the world, but can alter observer perception of distant parts of the world
A's conclusion is based on his perception of time. All processes involving em transactions occur at decreasing rates as material systems move at increasing speeds. This includes biological clocks.

U will measure the A ship as length contracted due to its motion.

A will measure the world as length contracted due to his perception.

 

scfi-lc-8-20.gif.b5c5a993509132795dda8d181271fef1.gif

 

 

Edited by phyti
Link to post
Share on other sites
  • Replies 62
  • Created
  • Last Reply

Top Posters In This Topic

Top Posters In This Topic

Popular Posts

There's no paradox. You're talking about a finite spacetime that seems to be flat. Or basically an object with a proper length of over ten billion light years. You're calling that "the universe", whic

So I will try to answer my own question since you didn't. Google tells us that the diameter of our visible universe is 8.8 x 1026 metres. Suppose this ship flew left to right across our visi

Have to factor in expansion as well. For distant destinations, the distance is growing at a rate faster than the ratio c.  

Posted Images

1 hour ago, phyti said:

U will measure the A ship as length contracted due to its motion.

A will measure the world as length contracted due to his perception.

The two frames are equivalent, the same reasons for length contraction apply equally to both of them.

Motion is relative. If A is in motion relative to U, then U is in motion relative to A.

Only moving things* are length contracted. If A measures "the world" as length contracted, then the world is moving relative to A. Any part of the world not moving relative to A, won't be length contracted according to A.

 

* Or, trying to be more accurate: "the lengths of, and distances between, objects as measured in their rest frame, are contracted in frames in which they're moving".

Edited by md65536
Link to post
Share on other sites

Another small point here.

Although the universe will appear to be 11 metres long to the pilot in the direction of motion,

in a direction at right angles to this the universe will appear to extend to its usual limits, whatever they may be.

Link to post
Share on other sites
20 hours ago, studiot said:

Another small point here.

Although the universe will appear to be 11 metres long to the pilot in the direction of motion,

in a direction at right angles to this the universe will appear to extend to its usual limits, whatever they may be.

And what about time dilation?

Link to post
Share on other sites
20 hours ago, Strange said:

Time doesn't have a directional component

Exactly.

However length contraction & time dilation go hand by hand, you cannot have the one without the other.

So I reiterate my question: what about time dilation when the observer sees a universe that as you states "will appear to be 11 metres long to the pilot in the direction of motion", but

"in a direction at right angles to this the universe will appear to extend to its usual limits, whatever they may be" ?

Link to post
Share on other sites
11 minutes ago, michel123456 said:

Exactly.

However length contraction & time dilation go hand by hand, you cannot have the one without the other.

So I reiterate my question: what about time dilation when the observer sees a universe that as you states "will appear to be 11 metres long to the pilot in the direction of motion", but

"in a direction at right angles to this the universe will appear to extend to its usual limits, whatever they may be" ?

It is a rotation between the time dimension and one spatial dimension (the one corresponding to the direction of travel)

Link to post
Share on other sites
1 hour ago, michel123456 said:

However length contraction & time dilation go hand by hand, you cannot have the one without the other.

And of course relativity of simultaneity, which is directional. A pair of clocks placed on a line perpendicular to their direction of motion remain synchronized with each other.

Please work through an example of this on paper or numbers. Put it into geometry or use equations. You can reiterate the same philosophical questions for 10+ years and still not be any closer to a philosophical understanding of the answers.

For example, suppose you have a stick 1 light second long, and you send light from one end (event A) to the other (B) and back (C). In the rest frame of the stick, the time between A and C is two seconds. In a frame where the stick is moving perpendicular to its length, A and B can be very far apart (many light seconds or even light years) because the stick moves, even without the stick's length changing. It can take much longer for the light to go from A to C, yet a clock on the stick only records 2 seconds during that time. There you have time dilation without length contraction. Then add a stick moving parallel to its length and see how length contraction is now needed. Draw this out on paper and if it still makes no sense, show the numbers that you're having trouble adding up.

Link to post
Share on other sites
13 hours ago, md65536 said:

And of course relativity of simultaneity, which is directional. A pair of clocks placed on a line perpendicular to their direction of motion remain synchronized with each other.

Please work through an example of this on paper or numbers. Put it into geometry or use equations. You can reiterate the same philosophical questions for 10+ years and still not be any closer to a philosophical understanding of the answers.

For example, suppose you have a stick 1 light second long, and you send light from one end (event A) to the other (B) and back (C). In the rest frame of the stick, the time between A and C is two seconds. In a frame where the stick is moving perpendicular to its length, A and B can be very far apart (many light seconds or even light years) because the stick moves, even without the stick's length changing. It can take much longer for the light to go from A to C, yet a clock on the stick only records 2 seconds during that time. There you have time dilation without length contraction. Then add a stick moving parallel to its length and see how length contraction is now needed. Draw this out on paper and if it still makes no sense, show the numbers that you're having trouble adding up.

??? (the bold part)

My question arises from the fact (fact?) that length contraction is directional while time dilation is not (?).

I used to understand it from the point of vue of an observer in FOR1 looking at another observer moving in FOR2, in which case there is no philosophical question: time dilation & lenght contraction mix in a perfect way.

My question arises when an observer, in some  FOR3, observes a universe contracted in his direction of motion. If time dilation has no directional component it gets awfully weird.

I wonder if the "observes a universe contracted in his direction of motion" is a correct statement. If this was correct, all observers could detect such a kind of observational contraction & thus could detect some "direction of motion" through the universe, which sounds weird to me.

Link to post
Share on other sites
13 hours ago, phyti said:

Length contraction is a change in the em forces that bond molecules. This phenomenon is observed in objects with a motion relative to the observer.

In the middle view, only the objects are lc. The space between has no material composition, thus no bonds. The objects are independent of each other, and not a composite object.

The issue of space between objects does not occur in the typical two system comparison, such as K and K'.

Relativity is taken into account into modern treatments of bonding, starting with Dirac's equation.

But, considered as speeding point charges and masses, electrons are not moving fast enough for the drastic and dramatic scenerios postulated by winterlong.

55 minutes ago, michel123456 said:

I wonder if the "observes a universe contracted in his direction of motion" is a correct statement. If this was correct, all observers could detect such a kind of observational contraction & thus could detect some "direction of motion" through the universe, which sounds weird to me.

There is always one frame in which no length contraction is observed.

An interesting related quesion is

"If the pilot and spaceship observe the universe contracted to 1m, how small does that make the observed size of the spaceship/pilot from the point of view of the universe"

Makes the ship in Asimov's Incredible journery gigantic?"

:)

Edited by studiot
Link to post
Share on other sites
7 hours ago, michel123456 said:

??? (the bold part)

My question arises from the fact (fact?) that length contraction is directional while time dilation is not (?).

It is, though. There is only one component of time in the velocity four-vector, so only that component can be affected. IOW, you can only go one direction in time.

 

 

Link to post
Share on other sites
6 hours ago, studiot said:

"If the pilot and spaceship observe the universe contracted to 1m, how small does that make the observed size of the spaceship/pilot from the point of view of the universe"

I roughly calculated an order of magnitude somewhere between a Planck length and a quark. It depends on how big you say the universe is. There are many orders of magnitude between Planck length and quark though; it would be around some billionths the size of a quark, and some billions of Planck lengths.

Link to post
Share on other sites

Create an account or sign in to comment

You need to be a member in order to leave a comment

Create an account

Sign up for a new account in our community. It's easy!

Register a new account

Sign in

Already have an account? Sign in here.

Sign In Now

×
×
  • Create New...

Important Information

We have placed cookies on your device to help make this website better. You can adjust your cookie settings, otherwise we'll assume you're okay to continue.