World Science Scholars

35.3 The Pole in the Barn: Lock the Doors

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    • What if Team Barn grabs the pole simultaneously not from their own perspective, but from Team Pole’s perspective? According to Team Pole, if the length of the pole is before the grab, what is its length after the grab? According to Team Barn, what is the length of the pole before and after the grab? (Hint: Does the pole get compressed or stretched?)

    • If the the length of the pole is (L) from Team Pole’s perspective, it will remain (L) from their perspective after Team Barn simultaneously grabs hold out of it. Team Barn, however, measures the pole’s length to be (L/gamma) before their members grab it, and (L*gamma) after they grab it.

      Explanation: Let us think about the two members of Team Barn who grab the front and the rear of the pole. Since the length of the pole is (L) from the perspective of Team Pole, then the distance between these two members from Team Pole’s perspective must be (L) as well to be able to grab the pole simultaneously. This distance between these two members will not change from Team’s Pole perspective after grabbing the pole. That is why the length of the pole will remain (L) from the perspective of Team Pole after it is grabbed.

      Team Barn’s Perspective of this scenario is quite different. The two members of their Team are a distance (L.gamma) apart, but the pole’s length is (L/gamma). One of these members holds the rear of the pole’s first (say at 7:00 PM on the rear clock), then the front of the pole continues to move until the other member holds it (at 7:00 PM on the front clock). That indeed makes sense because the clock at the pole’s rear is ahead of that at its front from Team Barn’s perspective.

      Mathematical Details:
      A) Before the pole is grabbed:
      – Team Pole’s perspective: pole’s length is (L).
      – Team Barn’s perspective: pole moves and Lorentz contracted. Pole’s length is (L/gamma).

      B) After the pole is grabbed:
      – Team Pole’s perspective: pole’s length is (L). The pole is stretched by a factor of gamma, but they measure its Lorentz contracted length so the gamma factors cancel.
      – Team Barn’s perspective: the pole is stretched. Pole’s length becomes equal to the sum of the initial length before grabbing and the stretched length (L/gamma + v*vL*gamma/c^2) = L(1/gamma + (v/c)^2 gamma) = L.gamma.

    • I agree with Andrew

    • Since dt’ = 0, then pole’s length won’t change. The persons at the back of the barn (clocks are ahead) will start first grabbing and therefore the barn will be stretched until the last one (person in front of the barn) grabs the pole.

    • i agree with andrew’s explanation as well

    • Andrew’s detailed explanation is completely convincing.

    • Confusing, but it appears that the pole would be stretched.

    • According to the Pole perspective, it does not change (as it is grabbed simultaneously). According to the Barn perspective, the pole gets stratched by factor gamma^2. Before the grab the length of the Pole from the Barn’s perspective was L_0 / gamma (due to usual Lorenz contraction).
      Aterthe grab we get something like this. Let the Barn coordinates be unprimed and the Pole coordinates – primed. delta_t’ = 0, delta_x’= L_0, as the Pole is grabbed simultaneously from its perspective, and we use rest length for delta_x’. Using Lorenz transformation we get: delta_x = gamma * (delta_x’ + 0) = gamma * L_0 – that is the distance from Barn’s perspective.
      So we get L_0 / gamma before the grab and L_0 * gamma after, therefore the factor is gamma^2, just as in the compression case.

    • If you measure in the same frame of reference as the pole (that is using the same now slice) you will get the correct value for the length (the so called “proper” length). The measurement is coupling two events (location front and back of the pole at this moment). However if you measure using a different now slice (which is the case if you are moving with respect to the pole) you will measure a different incorrect value. NOTHING HAS HAPPENED TO THE POLE IT HAS NOT CONTRACTED OR EXPANDED. The value measured is different but no physical contraction is taking place – we are simply using a different now time slice to carry out are measurements.

      It really is this simple. You are measuring using an invalid now time slice. The Lorentz contraction simply gives you a way of calculating how far you are off in your measurement. No genuine physical contraction takes place.

      Besides the fact that it is difficult to intuitively accept that objects are being physically squeezed there are other phenomena which are difficult to accept presented below which would take effect if distance is physically shortened.

      There is a lot of discussion about what Loentz contraction really is, with a significant group claiming that actual contraction of distance takes place (it is a space-like phenonemon) and another significant group stating that what is really happening (and being described) is that time dilation is taking place (it is a time-like phenomenon).

      Speed = Distance/Time is something everyone agrees on. What is apparently up for grabs is whether it is valid to invert the expression in order to define distance as Distance = Speed x Time or whether this inversion breaks down in a relativistic context where time is dilating.

      If it really is distance then one would need to account for apparent size. Apparent size is a property of distance: when you get closer to an object that object will appear larger. If Lorentz contraction really shortens distance (that is, it is a space like phenomenon and not a time-like phenomenon) then as Lorentz contraction takes place we would get physically closer to the object. By travelling ever closer to the speed of light we could get arbitrarily close. We should then see the object at the distance dictated by the Lorentz contraction. If Lorentz contraction really equates to shorter distances then theoretically, we could even observe a star as being a mile away or even closer (with all its detail!) that is a billion years distant in the rest frame. I do not accept that this is possible so I do not accept that length contraction equates to physical distance shortening.

      There are also other properties affected by (true) distance. Radiation intensity and gravitational pull to name two. If we are truly at just 1 mile distance from a star if we accelerate to the appropriate velocity then if we believe the space-like interpretation of Lorentz contraction we will experience the star just as if it were 1 mile away in a non-accelerated situation. We would be both fried and experience an extremely strongly gravitational pull.

      Note that the apparent size phenomenon is not the same as magnification. A space-like interpretation of the Lorentz contraction postulates that at the right velocity (very close to light) the distance will really be one mile and the observer (in the rocket presumably) will observe exactly the same thing as we would here on Earth if the star were 1 mile away. Magnification presents resolution issues which do not play a role in the apparent size case. If resolution issues are raised to prevent being able to see the star up close then the Lorentz contraction cannot be true distance shortening.

      In my view, Lorentz contraction is a (highly) useful mathematical method for manipulating time dilation (which is a real physical phenomenon) but the Lorentz contraction does not result in actual shortening of the physical distance. Objects and distances do not physically shrink (in the direction of motion or any other direction), a photon is not “everywhere in the universe” and we cannot define Distance to be Speed x Time in a relativistic context.

    • SRT allows for great cosmic humour in the pole in barn scenario.

      Team barn grabs the pole when it fits the barn. It stays short in team pole perspective.

      The length of the pole after the grab by team pole is too long – enlongated. .. even spaghettified?

      Team barn grabs the pole after it is compressed.

      Laurel and Hardy didn`t know what they were missing.

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    • from their perspective they would have to watch the clocks on the pole to grab so the pole will keep moving while they each take turns grabbing the pole when timer reaches x, so some of them will be outside by the time the others all grab the pole. the pole itself will still be the same length. that is from my own perspective so as my wife would say ‘it’s wrong’.

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