World Science Scholars

16.4 Motion’s Effect on Space

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    • Imagine you are standing on a platform, waiting for your train to arrive (the same train that George happens to be on). In the distance, you notice a beautiful mountain with the silhouette of an isosceles triangle (after all, you’re traveling in Switzerland, where Einstein developed special relativity). George also sees this exquisitely symmetrical Alp from his train window. Do you and George agree on the slope of the sides of the mountain (i.e., the angle of inclination relative to the horizontal axis)? Why?

      • slope=tan(theta)=height/base
        According to special relativity length perpendicular to the motion will not change. So, the height of the triangle will remain same. But as the motion is parallel to the base the base will be lorentz contracted from the perspective of the person in train. So, from the the perspective of the person in the train the slope of the triangle will be greater than from the perspective of the person on the platform.

      • we will see the same silhouette because a silhouette is always going to be perpendicular to the motion. if we were seeing a shadow, while we are both facing the sun, then george and i would disagree and george would see a shadow with less slope

      • We would agree on the slope of the mountain to be relatively the same, but the faster that George’s train travels the more significant the distortion. Only when we approach the speed of light, and at a significant fraction of it, does distortion become more noticeable, then we would not agree on the slope. It is all relative and is entirely dependent on the speed of either observer against each other. If we were splitting hairs then there would be a difference. But at the current rates of velocity, neither of us would be able to visually tell the difference.

      • No, George and I would not agree on the slope of the sides of the mountain. According to the principles of special relativity, the phenomenon known as length contraction or Lorentz contraction occurs when an object is observed from a moving frame of reference. The length of an object in the direction of motion appears shorter when measured from the perspective of an observer in motion relative to the object.
        In this scenario, as George is on a moving train while I am standing on the platform, George’s perspective is that of a moving frame of reference. Due to Lorentz contraction, the length of the mountain in the direction of George’s motion would appear shorter from his train window compared to what I observed from the stationary platform.
        Since the slope of the sides of the mountain is determined by the ratio of its vertical height to its horizontal length, the apparent shortening of the mountain, as observed by George, would result in an increase in the slope. Therefore, we would not agree on the slope of the mountain’s sides, as George would perceive a steeper slope due to the effects of Lorentz contraction.

    • Different perspective per Lorentz contracted. Perception is the key word, in all matters.

    • The mountain is moving from Georges perspective and so the horizontal distance between the top and bottom of the mountain is less in his frame of reference than in mine. Since the vertical distance is not in the same direction as George’s motion, he and I will agree on the vertical distance between the top and bottom. Therefore, as he measures the same height but a different length, he must also measure a different slope.

    • I see less steep slope.

    • George sees a steeper slope because the base of the triangle appears shorter to him.

    • No we don’t agree, my perspective the mountain is at rest as am I. George is on a moving train which he claims is at rest and the mountain is moving and appearing contracted to George therefore he sees a different angle.

    • We will not agree. While I see an isosceles triangle, George will see a triangle titled forward but with the same hight. The reason is as follows. We know that the triangle will shrink in the direction of motion (horizontally) but not in the vertical direction. Each of the two equal sides of the triangle consists of two components: vertical and horizontal. The horizontal component will shrink, but the vertical one won’t. Moreover, for the front side, the horizontal component will shrink more than the horizontal component of the rear side of the triangle. The base of the triangle will shrink horizontally. Hence, the result is that the triangle will be tilted forward with the same hight: the front side will be shorter and its angle with the base will be larger, while the rear side will be longer and its angle with the base will be smaller, and the base will be shorter.

    • If the motion is perpendicular to the plane of the triangle the contraction will have no influence on the shape of the triangle. Therefore they will agree on the slope. If the motion is not perpendicular to the plane of the triangle they will not agree on the slope due to the Lorentz contraction.

    • I do not understand the given numbers and numerical results, with such a low velocity as 30m/sec in the example of George and Sarah when measuring the length of the passing train and discussing the length contraction: the result should be derivable by applying the Lorentz contraction formula. Is there a mistake in these numbers (specially, the velocity of the train)?

    • NB a paradox and a contradiction are different notions.

    • Visions differ slightly. I’m seeing all in normal way but George sees it differently. Radicality of George’s view depends on velocity of the train.

    • The horizontal lengh of the mountain will appear shorter the one in the train, since it is relativaly moving respect to him, and not movin to ones in the staion.

    • George will see steeper slopes as the mountain is a bit shorter at the base along his direction of motion.

    • The triangularity of the mountain are its height and width – these are dimensions that are perpendicular to its apparent motion and thus do not exhibit Lorentz contraction.

      • When I wrote this (late at night) I assumed that George was looking out from the front of the train at the approaching mountain! From this perspective the mountain would exhibit that peculiar lensing, tunnel vision aspect, but be otherwise geometrically stable…? However, from a carriage window the view of passing scenery would be subject to Lorentz contraction and the mountain would appear to be the same height but steeper – more of a climbing/skiing challenge! But the snow would not fall off.

    • George will measure a different horizontal length of the mountain because it will be Lorentz contracted in George’s direction of motion, therefore he will measure steeper slopes.

    • no

    • Since the frame of reference is same for both they will agree for the same

    • The mountain is moving with respect to George, so his perception of length is different, so the slope is different.

    • yes, we would as the angle on inclination is perpendicular to the direction of motion of the train

    • I think NO the height and diameter perpendicular to of mountain remain unchanged but the diameter of mountain parallel to train motion changes

    • No. George will see a much steeper slope than me because according to him the horizontal expanse of the mountain has decreased due to Lorentz contraction but there is no change in its height.

    • No

    • Since simultaneity is a concept that changes from one observer to another observer and therefore they gonna have different notion of simultaneity and measure different slope…

    • Can’t we say that when objects move then curve the space around them so it is this space that causes the bodies in motion to contract and the body is at rest it will curve the space to a little extend?

    • No, the angles will be different (more acute for George). The mountain is moving from George’s perspective, therefore it is Lorenz contracted for him. The height of the mountain stays the same, but the length of the base of the mountain will be shorter for George, which results in a more acute angle – a steeper slope.

    • George sees steeper slopes. He claims his mountain is Lorentz contracted horizontally (in the direction of the train motion).

      Unless he’s in free fall together with his train from a very high bridge, in which case he’d claim the opposite: at one point the mountain actually starts shrinking vertically and flattens out all slopes… Briefly. 😳

    • I have a question, okay I understand why Gracie measured that short length by the explanation of George but look whatever the actual case of Gracie’s perspective! She is stationary with respect to this train. Thus her clock should take more time than Goerge. So why does Gracie has a short length? Can you please explain to me from the perspective of Gracie?

    • No, George and i do not agree.

      Relative simultanity allows for the different perspective. Moving objects are subject to the Lorenz equation.

      I am at a non-motion station platform. Not moving an atom. No Lorenz equation for this lad. No speed, no Lorenz gamma designation.

      Georges-porgy is stationary inside the moving train. George rides the speedy iron horse required for calculating the Lorenz equation.

      Calculating the gamma factor (the symbol given to the Lorenz equation) requires a velocity. I am at rest, only, and am not under the stipulations of a Lorenz motion alteration.

      George`s direction of motion measures the bumper, i measure the headlights.

      Georgy has an angle of inclination- because measurements for a moving object are different in time, length and other physical properties.
      https://en.wikipedia.org/wiki/Orbital_inclination?wprov=sfla1

      The Lorenz is all about Georgy-porgy. He is the reason for the season.

      It is an isoceles triangle (45°x 45°x 90°). The angles also carries the 45°=135° factor.

      It will appear similar, but i measure it from the radiator grid, George measures it from the rear hitch and Georges has a Lorenge contraction.

    • The mountain is in the shape of a triangle – The base of the triangle is lorentz contracted but the height is not from Georges perspective in the moving frame.
      So the sides will look steeper in the moving frame relative to the stationary frame.

    • The base would appear shorter to George so the slope would change

    • No

    • No, because the moving observer measure contracted length in direction of train movement. The height component of the slope is same according to both, unmoving and moving observers.

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