Modern Physics view of Length Contraction?

[meBigGuy]

I've been told several times that length contraction is not "real" in the sense of material or its space actually contracting. How does modern physics (by that I mean what is being taught currently) view Bell's spaceship paradox. Will the string break? Why, if length contraction is not real. I also have a hard time with the extended lifetimes of Muons in the atmosphere if, from their point of view, space had not contracted.

 

[jtbell]

It basically comes down to one's definition of "real." Different people have subtly different ideas about what "real" means in this context.

 

[nitsuj]

I've been told several times that length contraction is not "real" in the sense of material or its space actually contracting.

Maybe ask them if time dilation is "real", in the sense that time "really" slows down.

Is what is measured by the observer more "real" then what is measured by the moving (contracted/time dilated) "body"?

Both would agree the string broke.

 

[ghwellsjr]

One of the "rules" we use in evaluating the calculations we get from applying Special Relativity is that values that change just because we view the same parameter from different Frames of Reference are not "real" since they are dependent on the arbitrary frame we select. Length contraction is frame dependent (as is time dilation) so we can never say that a given length is "really" contracted as the same length might get shorter in one frame and longer in another.

However, when a rigid object is accelerated so that its speed changes, every frame will say that its length changes. Remember, an acceleration in one frame can be a deceleration in another frame so a length that gets shorter as a result of an acceleration in one frame would get longer as a result of deceleration in another frame. Some frames will say it gets longer, some frames will say it gets shorter. So we can never say that its length "really" contracts, only that its length "really" changes.

When we talk about the acceleration of a rigid object, we usually don't get down to the details of exactly where the force of acceleration is applied, we usually treat the entire object as a single point with its location being specified by a single value and we assume that it will survive the acceleration and not be stressed to the point where we could actually detect any damage as a result of the acceleration. This allows us to describe the object as a single event at any given point in time so that we can easily transform its coordinates into other frames and "calculate" the length contraction without concern for whether a real object will survive the force of acceleration. This, of course, can only happen in thought problems.

However, if we talk about a rigid object being accelerated at more than one point, then we have to specify the object with more than one event and we can no longer ignore the effects of stresses. So if we specify the problem in one frame such that the multiple points of acceleration cause the length to be stressed to the point of fracture (because we say that it cannot survive that stress), then this has nothing to do with viewing the problem from different reference frames as they will all say the same thing.

So the bottom line is that lengths that change as a result of viewing them from different reference frames are not "real" but lengths that change as a result of a rigid object being accelerated are "real".

 

[nitsuj]

So acceleration defines what is "real" in this context?

I see no difference in the scenarios between acceleration & inertial in determining if length contraction is "real".

Seems odd to say if the body is accelerating (i.e. every other FoR would agree who is moving) then it is "real". perhaps the process of determining what is "real" is democratic.

Doesn't the string get a vote?

Or is that merely the way physicists describe "real"?

 

[harrylin]

[..] perhaps the process of determining what is "real" is democratic.

Yes you could say that.
If according to measurements with all inertial reference systems a change of length occurs, then there is universal agreement about the reality of that occurrence - even though there is disagreement about the value of that change of length.

Doesn't the string get a vote?

The string breaks; isn't that telling?

Or is that merely the way physicists describe "real"?

As already mentioned, "real" isn't a well defined term among physicists.

 

[nitsuj]

The string breaks; isn't that telling?

Yea, that's why I wonder why the definition of "real" is ambiguous in this context.

Anyhoo, no difference if I think length contraction is really a "real" relativistic effect.

Thanks for the reply harrylin!

Hmmm... thinking of the string some more, the "at rest" FoR and moving "body" FoR would disagree on the length of the string/distance between ships. i.e. it broke for different reasons, with neither being wrong from a physics perspective.

The string "really" broke because it shrank (at "rest" FoR), the string "really" broke because the distance between ships increased (in motion FoR), I think that's right.

Looks like the only way to argue that it is "real' is to [STRIKE]determine[/STRIKE] assign a preffered/privileged FoR, Earth would get the most votes I'm sure .

 

[Meir Achuz]

I've been told several times that length contraction is not "real" in the sense of material or its space actually contracting. How does modern physics (by that I mean what is being taught currently) view Bell's spaceship paradox. Will the string break? Why, if length contraction is not real. I also have a hard time with the extended lifetimes of Muons in the atmosphere if, from their point of view, space had not contracted.

Try http://arxiv.org/abs/0906.1919

 

[ghwellsjr]

So acceleration defines what is "real" in this context?

I see no difference in the scenarios between acceleration & inertial in determining if length contraction is "real".

Seems odd to say if the body is accelerating (i.e. every other FoR would agree who is moving) then it is "real". perhaps the process of determining what is "real" is democratic.

Doesn't the string get a vote?

Or is that merely the way physicists describe "real"?

It's no different than talking about whether a body is at rest or in motion, it's frame dependent. But there is no inertial frame in which an accelerated body can be at rest both before and after the acceleration. So in a frame in which the body ended up at rest, its length gets longer, not shorter. Would you call that length contraction?

Now as to the string, if you set it up in a frame such that it breaks because it wants to contract but the accelerating spaceships won't let it contact, there are other frames in which it wants to expand, but it still breaks because the forward spaceship takes off before the rear one.

 

[nitsuj]

It's no different than talking about whether a body is at rest or in motion, it's frame dependent. But there is no inertial frame in which an accelerated body can be at rest both before and after the acceleration. So in a frame in which the body ended up at rest, its length gets longer, not shorter. Would you call that length contraction?

Now as to the string, if you set it up in a frame such that it breaks because it wants to contract but the accelerating spaceships won't let it contact, there are other frames in which it wants to expand, but it still breaks because the forward spaceship takes off before the rear one.

Yea I eventually came to a simular conclusion, see my above post. #7.

The arrogance of my FoR is tough to shake sometimes lol.

 

[ghwellsjr]

Looks like the only way to argue that it is "real' is to [STRIKE]determine[/STRIKE] assign a preffered/privileged FoR, Earth would get the most votes I'm sure .

The Earth is not an inertial frame so it doesn't qualify. Besides, we're talking Special Relativity where we ignore gravity and there is no such place in the universe where that qualifies. I prefer to educate people about Special Relativity. It is really a very simple concept with very easy math that anyone can understand who takes a small bit of effort.

 

[ghwellsjr]

Yea I eventually came to a simular conclusion, see my above post. #7.

The arrogance of my FoR is tough to shake sometimes lol.

Your FoR is not inertial either.

 

[nitsuj]

The Earth is not an intertial frame so it doesn't qualify. Besides, we're talking Special Relativity where we ignore gravity and there is no such place in the universe where that qualifies. I prefer to educate people about Special Relativity. It is really a very simple concept with very easy math that anyone can understand who takes a small bit of effort.

Yea to your point I'm idealizing.

Please elaborate on your last comment.

And I am suprised you missed my point regarding a preffered FoR, oh wait you didn't you just split hairs/introduced some specifics into the idealized scenario.

 

[ghwellsjr]

Please elaborate on your last comment.

Do you mean this comment?

It is really a very simple concept with very easy math that anyone can understand who takes a small bit of effort.

 

[nitsuj]

Do you mean this comment?

yea that one; It is really a very simple concept with very easy math that anyone can understand who takes a small bit of effort.

It seems to imply something

 

[ghwellsjr]

yea that one; It is really a very simple concept with very easy math that anyone can understand who takes a small bit of effort.

It seems to imply something

Special Relativity is very simple to understand, especially if you learn it from Einstein in his 1905 paper. What makes it so difficult is that many people have so many misconceptions about it that they have to first unlearn and then relearn.

 

[nitsuj]

Well, the comment couldn't be anymore subjective.

 

[meBigGuy]

Clem, the Franklin paper described the concept of 4 dimensional rotation, which is sort of how I have always thought of it (I aways thought of it as a "spatial distortion" that is inherent in the fabric of space). It's clear to me that the length of moving bodies actually change in the reference frame. It is not an "apparent" change. I'm still not exactly clear as to why the string breaks immediately though. I'll have to read it more carefully, as I pretty much skimmed it. I actually expected him to say it wouldn't break. Thanks for that one.

People age differenty in the direction of acceleration, so lengths change also. I need to work through it.

 

[ghwellsjr]

People age differenty in the direction of acceleration, so lengths change also. I need to work through it.

Aging occurs without regard to direction.

 

[meBigGuy]

Aging occurs without acceleration or relative motion also. Seems to come along with existence. Sometimes considering the context goes a long ways.

I was saying that identically accelerated objects age differently in the direction of acceleration.

 

[ghwellsjr]

I was saying that identically accelerated objects age differently in the direction of acceleration.

And I was saying "Aging occurs without regard to direction."

 

[pervect]

As has been noted, "real" isn't a well defined term. One element often associated with reality is "observer independent" or "frame independent" quantites. These are quantites that have the same value no matter what frame of reference one is in.

It is tempting, but probably overly ambitious, to say that quantites that depend on the observer aren't real.

For example, by this definition kinetic and total energies in Newtonian mechanics wouldn't be "real", because it's observer dependent. If you look at a closed, isolated system in Newtonian mechanics all observers will agree that energy of the closed system conserved, but different observers will give different values to this conserved energy - because the kinetic energy of an object depends on the observer, and the kinetic energy is part of the total energy.The concept of distance, and the concept of "now", were, before relativity, both regarded as being observer independent. Post-relativity, both the concept of distance and the concept of "now" are regarded as being dependent on the observer, though the observer dependence only becomes obvious at high velocities.

You may occasionally see remarks trying to summarize this that say "distance isn't real" and "now is an illusion", but that's rather over-ambitious, much like saying that energy isn't real because different observers don't agree on it's value. It's more helpful to say that "distance is observer dependent" and "now is observer dependent".

The good news is that there is an observer independent quantity in relativity. This is known as the Lorentz interval. So if you like to think of observer independent quantities as "really real", you can think of the Lorentz interval as being "really real".

 

[Meir Achuz]

It's clear to me that the length of moving bodies actually change in the reference frame.

What is your definition of "the length of moving bodies"?

 

[nitsuj]

Aging occurs without regard to direction.

Pretty sure meBigGuy is referring to comparative aging. with the observations being symmetric how is this "regardless of direction"?

 

[nitsuj]

What is your definition of "the length of moving bodies"?

Maybe the same hurdle I had, assuming a preferred/privileged FoR.


Although his/her statement is qualified with "it's clear to me". So there's how he/she defines it.

 

[MikeLizzi]

Special Relativity is very simple to understand, ...

Smart people understand a lot of things. But they will never understand what it is like not to be smart.

 

[harrylin]

Smart people understand a lot of things. But they will never understand what it is like not to be smart.

Only a genius is smart in all things. so, happily, most people do understand what it is like not to be smart in some field (My problem area: QM).

 

[ghwellsjr]

Smart people understand a lot of things. But they will never understand what it is like not to be smart.

I was talking about the math of Special Relativity being easy to learn as opposed to the math of General Relativity. Post #11 is where this all started:

The Earth is not an inertial frame so it doesn't qualify. Besides, we're talking Special Relativity where we ignore gravity and there is no such place in the universe where that qualifies. I prefer to educate people about Special Relativity. It is really a very simple concept with very easy math that anyone can understand who takes a small bit of effort.

 

[MikeLizzi]

I was talking about the math of Special Relativity being easy to learn as opposed to the math of General Relativity. Post #11 is where this all started:

I was talking about Special Relativity too.

 

[Meir Achuz]

And I was saying "Aging occurs without regard to direction."

People at the front of an accelerating spaceship age slower than those at the back.
If the equivalence principle is invoked, this is equivalent to gravitational reddening.

 

[ghwellsjr]

People at the front of an accelerating spaceship age slower than those at the back.
If the equivalence principle is invoked, this is equivalent to gravitational reddening.

Those people are not accelerating identically.

 

[ghwellsjr]

I was talking about Special Relativity too.

What math of SR would you say is not simple?

 

[Agerhell]

Only a genius is smart in all things. so, happily, most people do understand what it is like not to be smart in some field (My problem area: QM).

Formally, a genius is someone who understands something of value that nobody have understood before.

 

[Agerhell]

I've been told several times that length contraction is not "real" in the sense of material or its space actually contracting. How does modern physics (by that I mean what is being taught currently) view Bell's spaceship paradox. Will the string break? Why, if length contraction is not real. I also have a hard time with the extended lifetimes of Muons in the atmosphere if, from their point of view, space had not contracted.

I would say that out of the three things, time dilation, mass increase and length contraction we normally attribute to relativity, length contraction is the least real.

Time dilation is, as the GPS system is living proof of, very real.

Mass increase (or relativistic momenta if you like) is very real in for instance accelerators.

Length contraction on the other hand is only used to explain some experimental findings, such as the Michelson-Morley experiment. Lifetimes of cosmic muons are also often explained using length contraction but could if you like be explained by the muons traveling with high speed compared to the Earth just like the GPS satellites are. There is one other example more closely related to classical electrodynamics where lengt contraction is used as an explanation but I do not at the moment know what it is.

Nobody has ever conducted any "Bell space-ship experiments", but you can of course speculate about it if you like.

 

[bobc2]

I would say that out of the three things, time dilation, mass increase and length contraction we normally attribute to relativity, length contraction is the least real.

Length contraction on the other hand is only used to explain some experimental findings, such as the Michelson-Morley experiment.

Experiments at the RHIC (Brookhaven Relativistic Heavy Ion Collider) have "seen" the nucleons inside gold nuclei contract to a thin disk configuration when moving at close-to-light speed. Gold nuclei, moving in opposite directions, are collided.

Hermann Weyl (Einstein's close friend and colleague) described the universe as 4-dimensional, populated by 4-dimensional objects, typically characterized by relatively short lengths in the X1, X2, and X3 dimensions while extending for billions and trillions of miles in the 4th dimension. He accounts for the "motion of observers" as the motion of consciousnesses moving along their 4th dimension world lines at the speed of light. After all, the 4-dimensional objects do not move at all, they are static--motionless as 4-dimensionl objects (as is the entire universe).

Using this model, the mechanism underlying length contraction is quite trivial: Observers moving at relativistic velocities with respect to each other simply "view" totally different 3-dimensional pieces of the same 4-dimensional objects. So, no--the objects don't really change--they don't really contract, shrink--they are static--unchangeable as 4-dimensional fixed objects. Observers are limited to a 3-dimensional view; their 4-D world lines are oriented at different angles, and their instantaneous world volumes cut across the 4-D objects at different angles (you can compute the cross-secton views using Lorentz transformations). Thus, different observers have different cross-section views of the same 4-D objects, which results in different "observed" lengths along their respective X1 axes, for example. This situation is shown in the sketches below.

Notice that the red and blue observer views along their respective X1 axes cut across the 4-dimensional beam at different angles, resulting in different "observed" lengths for each observer. The cross-section views shown for blue and red correspond to instaneous views peceived by red and blue consciousnesses at the instant the consciousnesses are located at those particular points along the respective 4th dimension world lines.