Why does length contraction only occur parallel to the direction of motion?

[zonde]

I can't see how the scaling argument has any value. Dosent the 'train crashing and not crashing' argument rule out scaling as a valid counter argument, leaving only the Lorentz transformations as the 'must' contraction?

You seem to miss important point about this scaling function - it is not frame independent. If you require that transformation is symmetric (you invoke principle of relativity) then scaling function is ruled out.
Speaking about 'train crashing and not crashing' argument, it can be solved without contradictions if you scale down when you perform transformation in one direction and scale up when you perform reverse transformation.
So the point is that you have to invoke physical principle i.e. principle of relativity to get to the Lorentz transformation.

 

[ghwellsjr]

I was trying to say that a train cannot, crash in one reference frame and not crash in another, the 'thing' we are labeling as a crash is still 'thing' regardless of how we measure it through mathematics. Is not the case as you see it?

If you are saying that an event (a crash) exists in all frames, then yes, that is correct. But then all events, even ones where nothing "happens" beyond a particular time at a particular place, exist in all frames.

Look, it's like saying that every temperature on the Fahrenheit scale exists on the Centigrade scale or like saying that every weight on the Imperial scale exists on the Metric scale. Frames are just coordinates that we use to pinpoint events, they can't change or have any influence on what is actually happening. Would you say that if you measure a temperature in Fahrenheit and then you calculate the temperature in Centigrade that you have performed two measurements?

 

[peterspencers]

Rightyho so your saying reality is the way it is, and we can superimpose an infinite number of names, measurements and interpretations onto it but this dosent change it. So in answer, we would be measuring once? Also would you say reality has one true set of principles that we may one day discover? Or would you say reality is so infinite, in every sence, that understanding will always be an illusion?

 

[harrylin]

I can't see how the scaling argument has any value. Dosent the 'train crashing and not crashing' argument rule out scaling as a valid counter argument, leaving only the Lorentz transformations as the 'must' contraction?

Yes, in post #20 I explained that on order to conclude "must", you need to add such an argument; your light clock calculation is not sufficient for that. Once more (I copy-paste):

"you could assume, for example, that the vertical contraction is gamma and the horizontal contraction gamma square. Then with zero time dilation your calculation will also work.

However (in addition to other examples already given), imagine that two identical high objects collide; from SR symmetry they should have identical damage. Or alternatively, imagine a very fast bullet going through a narrow tube; it must not be possible to know which one "moves absolutely faster", and neither can it be that the bullet is smaller than the tube and also bigger than the tube when it passes through, so that a collision happens and also doesn't happen."

Therefore, in order for the two postulates to hold, the Lorentz transformations appear to be the only solution.

But as I and others have explained this in so many posts, and you seem to understand this, I won't try to explain it again!

 

[ghwellsjr]

Rightyho so your saying reality is the way it is, and we can superimpose an infinite number of names, measurements and interpretations onto it but this dosent change it. So in answer, we would be measuring once?

The basic problem is that once light has left you, you cannot tell when it arrives at any particular location remote from you because you have nothing faster than light with which to track its progress. The best we can do is have the light reflect off of a distant object and see when it gets there but we are not really seeing when it gets there, we are seeing the total round-trip time that it takes for the light to get to the distant object and for the reflection to get back to us.

Whenever we do this, we get the same value of time for the round-trip for any given measured distance. The time will always be twice the distance divided by c. This is a measurement. But we cannot know if the light spent the same amount of time getting to the remote object as it did to get back. For all we know, it could have spent 1/4 of the total time getting there and 3/4 of the total time getting back. Or any other pair of ratios that add up to one. Nature will not reveal to us the answer to this question.

Now you might think that the issue could be resolved by taking a second clock identical to the one that we are using to make our measurement and after making sure they read exactly the same time, move it to the remote location. The problem is that if we then bring it back, the two clocks will have a different time on them and the difference is larger the faster we move the clock.

But then you might think that if we move it slow enough, we can minimize the difference between the two clocks (after we bring the second clock back), which is true but we still don't know if when we get the clock to the remote location, which will take a certain amount of time as measured on the moving clock, that it takes the same amount of time as measured on the moving clock, to bring it back.

Einstein showed us the way out of this dilemma. We simply define time on the remote clock such that the light takes the same amount to time to get to the remote object as it does to get back. So after adjusting our remote clock so that this is true, if we then measure when the light gets to the remote object, are we making a measurement, or simply reading back the time we previously put there? This process is the basis of defining an inertial Reference Frame in Special Relativity by expanding the process to an infinite number of imaginary clocks located at every position throughout space.

Now if someone else, moving inertially with respect to us follows the same process with his own set of rulers and clocks and we each "measure" the time and location of an event remote from both of us, we can get different answers but do you consider this difference to be somehow a difference in reality or even a difference in measurement, or rather merely a difference in definition?

Also would you say reality has one true set of principles that we may one day discover?

No, we've already discovered the one true set of principles.

Or would you say reality is so infinite, in every sence, that understanding will always be an illusion?

No, we have an excellent and concrete way of understanding it.

 

[peterspencers]

Yes, in post #20 I explained that on order to conclude "must", you need to add such an argument; your light clock calculation is not sufficient for that. Once more (I copy-paste):

Thankyou harrylin I finally see why this argument needs to be added :) The example on its own dosent encompass the equivalence principle and you need this to show why the Lorentz transformations are the only ones that fit the bill.

Thankyou for your patience in explaining that too me, I am incredibly grateful.

 

[harrylin]

Thankyou harrylin I finally see why this argument needs to be added :) The example on its own dosent encompass the equivalence principle and you need this to show why the Lorentz transformations are the only ones that fit the bill.

Thankyou for your patience in explaining that too me, I am incredibly grateful.

You're welcome!

Note that "equivalence principle" is something else (related to general relativity); here we discussed the relativity principle of special relativity.