Is There a Connection Between Planck Length and Planck Time in Relativity?

Click For Summary

Discussion Overview

The discussion revolves around the relationship between Planck length and Planck time within the context of relativity, exploring whether these quantities behave differently under relativistic effects such as time dilation and length contraction. Participants examine the implications of these fundamental units as they approach the speed of light, and whether they can be compared meaningfully.

Discussion Character

  • Exploratory
  • Debate/contested
  • Conceptual clarification

Main Points Raised

  • Some participants suggest that as relative speed approaches the speed of light, time dilation and length contraction occur at different rates due to the differing magnitudes of Planck length and Planck time.
  • Others argue that Planck length and Planck time are merely units of measurement, similar to meters and seconds, and that their relationship is defined rather than indicative of physical behavior.
  • A participant questions whether the numbers associated with Planck units are arbitrary and could have been defined differently, suggesting that this could affect their relationship.
  • Another participant introduces the concept of the gamma factor, stating that time dilation and length contraction can be calculated from the same dimensionless factor, implying they occur on the same scale.
  • There is a discussion about the behavior of light emitted from objects moving at relativistic speeds, with some participants seeking clarification on whether light moves in straight lines and referencing relativistic aberration.
  • One participant raises a question about the motivations behind astrophysicists' approaches to dark matter, linking it back to the earlier discussion on Planck units.
  • A follow-up question is posed regarding the energy required to reach Planck length and time, questioning whether infinite energy would be necessary to achieve such states.

Areas of Agreement / Disagreement

Participants express differing views on the significance and implications of Planck length and Planck time in relation to relativity. There is no consensus on whether these quantities can be meaningfully compared or how they relate to relativistic effects.

Contextual Notes

The discussion includes assumptions about the nature of measurement units and their implications in physics, as well as unresolved questions regarding the relationship between energy, speed, and fundamental limits in the context of relativity.

  • #31
This is probably repeating the same question, but i want to make sure it is:

I've watched the following 3 part video:


If we consider that g=h=c=1 and derive the meter, second and kg from them:

Does length contraction advance at the same rate as time dilation advances, as an object gets closer towards the speed of light?

Is the subject of arbitrariness now still what defines this question, as it was that defined it as originally expressed in this thread?
 
Physics news on Phys.org
  • #32
roineust said:
Does length contraction advance at the same rate as time dilation advances, as an object gets closer towards the speed of light?
Either I am misunderstanding your question or it was answered by @PeroK in post #8.
 
  • Like
Likes   Reactions: roineust and PeroK
  • #33
Nugatory said:
Either I am misunderstanding your question or it was answered by @PeroK in post #8.

How is it that an expression (gamma) that includes time and length in it, in the form of speed, is dimensionless?
 
  • #34
roineust said:
How is it that an expression (gamma) that includes time and length in it, in the form of speed, is dimensionless?
You can easily work out the units for yourself.
 
  • Like
Likes   Reactions: roineust
  • #35
roineust said:
How is it that an expression (gamma) that includes time and length in it, in the form of speed, is dimensionless?
Because it only involves ##v/c## and that is dimensionless.
 
  • Like
Likes   Reactions: roineust
  • #36
Is a single occurrence of light refraction in water, considered mathematically an addition of a dimension?
 
  • #37
roineust said:
Is a single occurrence of light refraction in water, considered mathematically an addition of a dimension?
Whatever you mean to say here, it's coming across as nonsense. Try to formulate your question more clearly. If it's a new topic, start a new thread.
 
  • Like
Likes   Reactions: Vanadium 50
  • #38
roineust said:
Does a single occurrence of light refraction in water, considered mathematically an addition of a dimension?
"Dimension" in this context is the physical dimensions of length ##L##, mass ##M## and time ##T##. For example, velocity has dimensions of ##LT^{-1}##,; force has dimensions of ##MLT^{-2}## and energy has dimensions of ##ML^2T^{-2}##.

This is not to be confused with spatial and time dimensions.

Something like ##\frac v c##, or ##\frac {m_1}{m_2}## which appears in a lot of mechanics problems, is dimensionless. This means also that these quantities are independent of the units. If the velocity is half the speed of light, then ##\frac v c = \frac 1 2## regardless of the units.

See:

https://en.wikipedia.org/wiki/Dimensional_analysis
 
  • Like
Likes   Reactions: roineust
  • #39
Maybe we could remove the arbitraryness of the original question regarding units by assuming a base measure of length as 1 Lightsecond = 299796 km = 1 Flash [f]. By using this base, the Planck-Length would become 0.53*10^-43 f. So why is it only roughly half the length that light could cover in 1 Planck-Time (1*10^-43 s)?
If you define your unit of length to only rely on your unit of time (which you can do since there is such a well defined, prominent speed...), then it becomes irrelevant what you mean by "1 Second" as well, the ratio still is roughly 2 Planck-Length = 1 Planck-Time. It might be "irrelevant" to ask why - but then, why's that?
 
  • #40
Thomas Sturm said:
So why is it only roughly half the length that light could cover in 1 Planck-Time (1*10^-43 s)?
It isn't - your value for the Planck time is off by a factor of roughly two. The Planck time is 5.39×10-44s, which is consistent with your Planck length in light seconds - as it must be by definition.
 
  • #41
"The Planck time is the time it would take a photon traveling at the speed of light to across a distance equal to the Planck length. " Is the, very sensible, answer to the original question, then. If I had just googled "planck time length" first...this was just such a "1st-post-idiocity" from me, it really made me laugh (and still smile as I type this, in a slightly embarrassed kind of way). Thank you Ibix.
"No. It just means that seconds are bigger than meters."
This just has to be the coolest answer, ever.
 
Last edited:

Similar threads

Undergrad Comparing Planck's Mass, Length, Time and Energy
  • · Replies 5 ·
Replies
5
Views
2K
High School Does Acceleration Affect Planck Lengths in General Relativity?
  • · Replies 3 ·
Replies
3
Views
1K
Undergrad Length Contraction & Time Dilation Beyond Planck Scale: Correct?
  • · Replies 4 ·
Replies
4
Views
2K
Graduate Speed of light and planck length
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad What causes time dilation and length contraction
  • · Replies 10 ·
Replies
10
Views
2K
High School Dimensional analysis peculiarity
  • · Replies 6 ·
Replies
6
Views
2K
Undergrad Subbing Planck length into length contraction equation?
  • · Replies 2 ·
Replies
2
Views
2K
High School Why does length contraction occur and how does it relate to time dilation?
  • · Replies 63 ·
3
Replies
63
Views
6K
High School Schwarzschild radius of an object is smaller than Planck length
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad Time difference caused by length contraction
  • · Replies 52 ·
2
Replies
52
Views
4K