How Do Lorentz Transformations Apply to Aircraft Communication Delays?

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In summary, the problem involves two aircrafts touching down at different times and a distance of 3.8x10^3km between them. The question is whether a signal sent by the first pilot after touchdown will reach the second pilot after his own touchdown. The distance and time values are given and the average speed of the signal can be calculated using the expression for v_{ave}. The problem involves considering the velocity of the aircrafts and whether the signal travels at a speed greater or less than the speed of light, c.
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Quelsita
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Ok, I think for this problem you have to use the Lorentz transformations, but I'm not sure how to consider the velocity.

Question:
At 9 hrs 0min 0sec an aircraft touches down in NY. At 9hrs 0min 0.01sec an aircraft touches down in San Francisco. The (straight) distance between the two is 3.8x10^3km.
a) show that any signal that thepilot of the first aircraft sends after the instant of touchdown will reach the second pilot after his own touchdown.

So, for this x=3.8x10^3km, deltat =0.01sec, but if the aircrafts are stationary, what is the velocity? If it is a singnal, is this just c?
 
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Quelsita said:
Ok, I think for this problem you have to use the Lorentz transformations, but I'm not sure how to consider the velocity.

Question:
At 9 hrs 0min 0sec an aircraft touches down in NY. At 9hrs 0min 0.01sec an aircraft touches down in San Francisco. The (straight) distance between the two is 3.8x10^3km.
a) show that any signal that thepilot of the first aircraft sends after the instant of touchdown will reach the second pilot after his own touchdown.

So, for this x=3.8x10^3km, deltat =0.01sec, but if the aircrafts are stationary, what is the velocity? If it is a singnal, is this just c?

Well, this one looks fairly easy...what is the expression for the average speed [tex]v_{ave} [/tex]of any signal that travels a distance [tex] {\Delta}x [/tex] in a time [tex] {\Delta}t [/tex]? If you plug in the distance above along with your [tex] {\Delta}t [/tex] how fast would the signal have to be? Is it greater or less than c?
 
  • #3


I would first clarify the context of the problem and ask for more information. Are we dealing with two stationary aircrafts or two moving aircrafts? If they are moving, what are their velocities? The Lorentz transformations are typically used in the context of special relativity, which deals with the effects of relative velocities on measurements of space and time. Without knowing the velocities of the aircrafts, it is difficult to apply the Lorentz transformations to this problem.

Assuming that the aircrafts are stationary, then yes, the velocity of the signal would be the speed of light (c). However, if the aircrafts are moving relative to each other, then we would need to consider the Lorentz factor and apply the appropriate transformations to calculate the velocity of the signal.

In order to show that any signal sent by the first pilot will reach the second pilot after his own touchdown, we would need to know the exact positions and velocities of the aircrafts at the time of touchdown. Without this information, it is not possible to accurately calculate the time it would take for the signal to reach the second pilot.

In summary, the Lorentz transformations can be a useful tool in calculating the effects of relative velocities, but without more information about the problem at hand, it is difficult to apply them accurately.
 

What are Lorentz Transformations?

Lorentz Transformations are a set of equations used in special relativity to describe the relationship between space and time for observers in different inertial frames of reference. They were developed by Dutch physicist Hendrik Lorentz in the late 19th century.

Why are Lorentz Transformations important?

Lorentz Transformations are important because they allow us to understand how measurements of space and time are affected by the relative motion between observers. They also form the basis for Einstein's theory of special relativity, which has had a profound impact on our understanding of the universe.

What is the Lorentz Factor?

The Lorentz Factor is a term used in Lorentz Transformations to account for the effects of time dilation and length contraction. It is represented by the Greek letter gamma (γ) and is equal to 1/√(1-(v/c)^2), where v is the relative velocity between observers and c is the speed of light.

Do Lorentz Transformations only apply to objects moving at high speeds?

No, Lorentz Transformations can be applied to any relative motion between observers. However, their effects become more significant at high speeds, approaching the speed of light. At everyday speeds, the differences between the measurements of space and time for different observers are negligible.

How do Lorentz Transformations differ from Galilean Transformations?

Lorentz Transformations take into account the constancy of the speed of light, which is a fundamental principle of special relativity. Galilean Transformations, on the other hand, assume that the speed of light is infinite and therefore do not accurately describe the relationships between space and time at high speeds.

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