Gravitational Time Dilation - Is my head older than my feet?

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Discussion Overview

The discussion revolves around the concept of gravitational time dilation as described by general relativity, specifically questioning whether a person's feet, being closer to the Earth, age more slowly than their head. Participants explore the implications of this phenomenon, seek mathematical explanations, and discuss the practical significance of the time difference.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • Some participants assert that due to gravitational time dilation, the feet, being closer to the Earth, would indeed be younger than the head at the time of death.
  • One participant requests clarification on the complexity of the mathematics involved in demonstrating this effect.
  • Another participant provides a link to a Wikipedia article as a resource for understanding gravitational time dilation calculations.
  • A participant expresses interest in contextualizing the time difference once a value for time dilation (Td) is obtained.
  • It is noted that while the time difference exists, it is very small due to the relatively weak gravitational field of the Earth compared to other cosmic bodies.
  • One participant shares their calculation of the time difference, estimating that their head is 180 nanoseconds older than their feet, based on their height and age.
  • Another participant questions the assumption that the head and feet would "die" at the same time, suggesting that the head might die first since time runs faster for it.

Areas of Agreement / Disagreement

Participants generally agree on the concept of gravitational time dilation affecting the aging of body parts differently based on their proximity to a gravitational source. However, there is no consensus on the implications of this effect regarding the timing of death or the significance of the time difference.

Contextual Notes

Participants express varying levels of understanding regarding the mathematical aspects of gravitational time dilation, with some noting the weak gravitational field of the Earth as a limiting factor in the observed effects. The discussion includes assumptions about standing upright since birth and the implications of time running differently for different body parts.

Awol_01010001
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According to general relativity, objects in a strong uniform gravitational field experience time slower that objects in a weak uniform gravitational field.

Does this mean that my feet, being closer to the Earth that my head, are younger than my head when I die?

If this is correct could someone oblige me in showing me the maths involved should it not be to complicated. Or at least link a source to be where I can learn these calculations for myself.

Kindest Regards,
 
Last edited:
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Awol_01010001 said:
Does this mean that my feet, being closer to the Earth that my head, are younger than my head when I die?

Yes, that's right. They experience stronger acceleration, and so are more time-dilated.
 
inottoe said:
Yes, that's right. They experience stronger acceleration, and so are more time-dilated.

Is the maths involved complicated to a lay person? i would like to be able to demonstrate this to others.
 
You could try this: http://en.wikipedia.org/wiki/Gravitational_time_dilation" . The maths isn't too complicated.
 
Last edited by a moderator:
That's very useful. One more question if you don't mind.

Once I have a value for Td how do I put this in context?

For example after my feet are 1 second old my head is y seconds old?
 
Yes you are correct. But remember, Earth's gravity is very weak (and gravity is already the weakest of the 4 forces) compared to most cosmic bodies. So its not like your head is years older than your feet, but by a very tiny amount of time. Great observation though.
 
abaio said:
Using the equation on Td = e^(gh/c^2) how would I express the difference in time after obtaining a value for Td?

This equation gives the ratio of the two times.
 
Last edited by a moderator:
Awol_01010001 said:
This equation gives the ratio of the two times.

Fantastic. Thanks for your help.

So I tried to calculate this. I took my height and approximate age (of my feet) in seconds to the nearest day.
And i used the linear "weak field" approximation Td = 1 + gh / c2 of the equation.

I calcualted that my head is 180ns older than my feet, assuming of course i have been standing upright since birth :smile:
 
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Looks fine, but don't you feel silly copying down 8 sig figs at intermediate steps in a 2-sig-fig calculation?
 
  • #10
How do you justify the asusmption that your head and feet die at the "same time"?

Couldn't you equally argue that your head would die first, since time runs faster for it?

;)
 

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