10.4 Motion’s Effect on Space
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August 8, 2019 at 12:03 pm
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?
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July 25, 2020 at 10:52 am
No; George and I will not agree on the slopes of the mountain. This is due to length contraction. If fact, if the base of the mountain is parallel to the direction of motion of the train, then George will see the mountain to have a steeper slope than I will see. This is because the horizontal component of the slope will contract from George’s perspective and this in turn increases the gradient (steepness) of the slope for George
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July 31, 2020 at 11:54 am
No, because the Horizontal length of mountain will appear shorter to George
As length perpendicular to direction of motion seems unaffected, so the slope will be more foe George than that for me. -
August 2, 2020 at 2:26 pm
No, because of Lorenz contraction will take place there.And the horizontal component of one side of that Mounten will be contracted along the direction of motion but the vertical component will remain unchanged ,so the angle between them Will increase.
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August 4, 2020 at 11:10 am
The answer is no due to the fact that Lorenz contraction will take place
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August 8, 2020 at 6:15 pm
No, the base of the mountain will appear shorter from George’s perspective keeping the same height. So for him sides will have stepper slopes than for us that we see the mountain at rest. Lorentz contraction
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August 9, 2020 at 1:13 pm
The Lorentz Contraction will skew George’s view of the (relative) stationary landscape around him. His view will be distorted by the stretching of space around him thus giving a much different view of the landscape. While the peaks’ heights will remain the same, the sides will be contracted in George’s direction of motion.
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August 11, 2020 at 2:49 am
George will find the isosceles included angle to be smaller, due to Lonentz contraction.
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August 17, 2020 at 5:56 am
Absolutely NO! Due to the length contraction, angle of the mountain differs for me and George, as the length contracts at the direction of the motion ( direction opposite to the velocity of the train relative to George) .So, the measurement of the slope of the mountain by me and George will not agree with each other.From George’s perspective, The Mountain would be steeper than it would be in my perspective.
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August 23, 2020 at 9:33 am
I knew the answer without reading everyone else’s response!
No – Lorentz Contraction
I love this stuff!
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August 24, 2020 at 10:47 am
If it is a traditional speed train then no perceived differences and the mountain and train will look the same to both observers.
However if the train is travelling close to the speed of light (e.g. due to new teleport/ warp drive technology?) then George should see a fixed length train and more Isosceles mountain with acuter peak angle. Meanwhile you on the platform will still see an Equilateral shaped mountain but with a length contracted train compared to the stationary equivalent.
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August 25, 2020 at 1:54 am
That depends. If I go to George’s perspective and measure it and vise versa, we might draw the same conclusions. Typically, the answer could also be no due to Lorentz contraction. Independently we will draw different conclusions and take different measurements. It’s all a matter of perspective.
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August 25, 2020 at 6:12 am
No, Because of Lorentz contraction that george is moving in a horizontal straight line than in the horizontal direction, space will look contracted to him,
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September 23, 2020 at 6:22 pm
I believe a distant isosceles shape, oriented in a plane perpendicular to the train’s motion, would look the same to both observers. The Lorentz contraction does not apply to measurements perpendicular to the relative motion, so the base length as well as the height of the triangular shape remain the same. If that is true, then then the slope of the sides also appears the same to both observers.
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February 7, 2021 at 2:10 am
I make this redundant reply, because it was asked in first post, and I don’t know the reason it was asked. So, in doubt, I reply, anyway. :shrug::
George and Grace see different slopes. George sees shorter triangle base, same height, because of his motion.
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February 24, 2021 at 9:35 pm
No, due to Lorentz Contraction ( to George ). In relation to me, the mountain does not move.l
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February 12, 2022 at 2:20 pm
No. George would see a shorter horizontal lenght – Lorentz Contraction
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July 6, 2022 at 12:37 am
There is no relative motion between myself and the mountain thus the perception of the mountain will be that of rest space. On the other hand, from George’s perspective, as he is in relative motion with regards to the mountain, he will be observing Lorentz contraction of the same mountain. This will mean that the angles between the horizontal and the sides of the isosceles increases.
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September 29, 2022 at 10:08 am
I am not in motion, the Lorentz transformations do not apply to me. Again, i am not on motion, so length contraction is not applicable.
SRT says the object in motion has all the chance to cheat time.If we all see the mountain as similarly proportioned, the angle of inclination increases as George gets closer. It does not increase at the station.
All the motion science apply to George, not me.
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July 17, 2023 at 4:08 pm
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. -
July 19, 2023 at 6:22 pm
No George wouldnt agree on the sides odf the mountain because of the Lorentz contraction occurring when an object is observed from a moving position of reference we will see distortion in the image point in this case the mountain. All motion is applied to George not to us the viewer
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November 11, 2023 at 2:32 am
No we don’t agree as george is on the train which is in motion and I am stationary at the platform,
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July 22, 2024 at 6:02 am
No, ya que las posiciones de observador, es decir la de George y la mía son diferentes y también actua la contracción de Lorentz.
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