Planck length and Planck time

In summary, the Planck length and the Planck time are simply units of measurement, and the numbers -35 and -43 are arbitrary in the sense that they are a result of defining what a meter and a second are. There is no specific reason for these numbers to be chosen other than convenience. Time dilation and length contraction can be calculated using the same gamma factor, and they are both observed to happen on the same scale. The relevance of an object moving at close to the speed of light is seen in relativistic aberration, which has been well measured and understood. Astrophysicists use theories that modify Newtonian dynamics rather than General Relativity dynamics to explain dark matter, and this choice may be due to the complexity of understanding experiments
  • #1
roineust
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If Planck length is 10^-35 of a meter and Planck time is 10^-43 of a second, doesn't that mean that as the relative speed gets closer to the speed of light and time acceleration and length contraction are happening, they are happening at a different rate, since length contraction has to reach all the way to 10^-35 while time acceleration has to reach all the way to 10^-43 ??

Yes, another kindergarten level mathematics question, nothing i can do or will ever be able to do about that, since I'm way past kindergarten age.
 
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  • #2
roineust said:
If Planck length is 10^-35 of a meter and Planck time is 10^-43 of a second, doesn't that mean that as the relative speed gets closer to the speed of light and time acceleration and length contraction are happening, they are happening at a different rate, since length contraction needs to reach all the way to 10^-35 while time acceleration needs to reach all the way to 10^-43 ??
No. It just means that seconds are bigger than meters.
 
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  • #3
Dale said:
No. It just means that seconds are bigger than meters.

You are saying that I'm trying to compare oranges and apples or are you saying something else?
 
  • #4
The Planck length and the Planck time are just units like meters and seconds, or furlongs and fortnights. A mathematical relationship between them tells us only that they’ve been defined in a way that produces that relationship.
 
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  • #5
Nugatory said:
The Planck length and the Planck time are just units like meters and seconds, or furlongs and fortnights. A mathematical relationship between them tells us only that they’ve been defined in a way that produces that relationship.

But isn't such a generalization possible, no matter what arbitrary basic unit of time and length we choose?
 
  • #6
Nugatory said:
The Planck length and the Planck time are just units like meters and seconds, or furlongs and fortnights. A mathematical relationship between them tells us only that they’ve been defined in a way that produces that relationship.

You are saying that -35 and -43 are arbitrary numbers in the sense that they are the result of the arbitrariness of deciding what is a meter and what is a second and it could have been easily arbitrarily chosen so that both reach a minimum amount together at -35 or both at -43 or both at any other number?
 
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  • #7
roineust said:
You are saying that -35 and -43 are arbitrary numbers in the sense that they are the result of the arbitrariness of deciding what is a meter and what is a second and it could have been easily arbitrarily chosen so that both reach a minimum amount at -35 or both at -43 or both at any other number?
Exactly!
 
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  • #8
roineust said:
If Planck length is 10^-35 of a meter and Planck time is 10^-43 of a second, doesn't that mean that as the relative speed gets closer to the speed of light and time acceleration and length contraction are happening, they are happening at a different rate, since length contraction has to reach all the way to 10^-35 while time acceleration has to reach all the way to 10^-43 ??

Length contraction and time dilation can be calculated from the same dimensionless gamma factor:
$$\gamma = \frac 1 {\sqrt{1- v^2/c^2}}$$
As far as it makes any sense to say so, time dilation and length contraction happen on the same scale.

The Planck quantities are irrelevant.
 
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  • #9
How do we know that as an object gets closer to the speed of light, the light it emits is still observed to move in straight lines? do we know it as a result of a thought experiment or as a result of an actual experiment?
 
  • #10
roineust said:
How do we know that as an object gets closer to the speed of light, the light it emits is still observed to move in straight lines? do we know it as a result of a thought experiment or as a result of an actual experiment?
How do you think it might move, if not in a straight line?

How would the source influence the light after it has left the source and is propagating through vacuum?

In what way would you modify Maxwell's equations to have light travel other than in a straight line?

What other physical principle would you invoke to justify light moving through vacuum other than in a straight line?

What's the relevance of the source moving at close to the speed of light?
 
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  • #11
roineust said:
How do we know that as an object gets closer to the speed of light, the light it emits is still observed to move in straight lines? do we know it as a result of a thought experiment or as a result of an actual experiment?
Relativistic aberration is well measured and understood.
 
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  • #12
Dale said:
Relativistic aberration is well measured and understood.

I get the impression that understanding experiments that involve light emitted from objects moving relatively to an observer at close to the speed of light, are generally much more complicated to understand, and therefore are pedagogically ignored when it is concerned with beginners, which are left only with train like thought experiments? Perhaps there exists a simple to understand experiment, that can be brought up as an example regarding such a subject?

I am saying this also because i went to the wiki entry relativistic aberration and it seems to include only an equation that results from a train thought experiment geometry, but does not seem to include any experimental examples.
 
  • #13
I think that the clearest evidence is in relativistic beaming. In massive objects that are accreting mass you get two funnels of very hot relativistically moving particles. Because they are moving relativistically the resulting radiation is highly anisotropic. That makes it so that if the “north” jet is pointed towards us it is far brighter than the “south” jet.
 
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  • #14
Why do astrophysicists try to solve the dark matter question by theories that modify Newtonian dynamics and not by theories that modify General Relativity dynamics?

This might sound like a weird and naive question, but i hope it is still legitimate to ask it.
 
  • #15
What does this have to do with the Planck length and time. (Your last question too)
 
  • #16
roineust said:
Why do astrophysicists try to solve the dark matter question by theories that modify Newtonian dynamics and not by theories that modify General Relativity dynamics?
Google TeVeS. They've just never managed to construct a plausible modification of GR, as far as I know.
 
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  • #17
Dale said:
What does this have to do with the Planck length and time. (Your last question too)

Since i read that the only change that MOND assumes, is that at a certain acceleration there is a cross over of inverse equation to an exponential equation and i wonder if such cross overs at certain acceleration or at certain constant speed were considered for relativity and if not, the reason why not might be interesting as well.

And although in a very wrong and mathematically error prone way, that was close to the motivation behind my initial question in this thread and the question about light behavior as it is emitted from objects moving close to the speed of light relative to an observer.
 
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  • #18
roineust said:
Why do astrophysicists try to solve the dark matter question by theories that modify Newtonian dynamics and not by theories that modify General Relativity dynamics?

They don't. And you're hijacking your own thread.
 
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  • #19
Dale said:
Exactly!

If the first question in this thread is physically not erroneous in the sense of combining relativity and Planck size, then here is a follow up question:

As much as i understood, one can never put enough energy in order to reach the speed of light, since there will be a need for infinite amount of energy. But one can get closer to the speed of light, every time he puts in more energy.

Thus, does this mean that in order to get to a Plank length & time, one needs an infinite amount of energy?

If not, how could that be? Wouldn't that mean that the relative time acceleration and length contraction, can go below the Planck length & time limit?
 
  • #20
roineust said:
If the first question in this thread is mathematically and physically not erroneous, then here is a follow up question:

As much as i understood, one can never put enough energy in order to reach the speed of light, since there will be a need for infinite amount of energy. But one can get closer to the speed of light, every time he puts in more energy.

Thus, does this mean that in order to get to a Plank length & time, one needs an infinite amount of energy?

If not, how could that be? Wouldn't that mean that the relative time acceleration and length contraction, can go below the Planck time length & time limit size?
Velocity is frame dependent. Theoretically, we can consider two IRF's moving with any relative velocity. We can consider, therefore, the length of a metre stick in our rest frame to have no minimum length in other IRFs.

The Planck length and time have no physical significance in respect of special relativity.
 
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  • #21
PeroK said:
Velocity is frame dependent. Theoretically, we can consider two IRF's moving with any relative velocity. We can consider, therefore, the length of a metre stick in our rest frame to have no minimum length in other IRFs.

The Planck length and time have no physical significance in respect of special relativity.

But wasn't there a whole conundrum in the past, regarding how physically real is length contraction? Doesn't this make either length contraction or Planck size limit not physically real?
 
  • #22
roineust said:
But wasn't there a whole conundrum in the past, regarding how physically real is length contraction? Doesn't this make either length contraction or Planck size limit not physically real?
I don't see any conundrum. Phrases like "physically real" in this context are dangerous words that can lead you away from any understanding of the physics. SR is self-consistent and the Planck length is irrelevant. That's all that's important.
 
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  • #23
roineust said:
Planck size limit
There is no known size limit.
 
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  • #24
roineust said:
But wasn't there a whole conundrum in the past, regarding how physically real is length contraction?

Not among physicists.
 
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  • #28
roineust said:
Ok, so more than a century ago there was some confusion by at least one little-known scientist (at least I never heard of him). That has been resolved since before I was born and before my parents were born and before my grandparents were born. This is not a point of confusion in the mainstream scientific literature.
 
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  • #29
roineust said:
Doesn't this make either length contraction or Planck size limit not physically real?
There is no Planck (or any other) size limit in relativity. My understanding is that the various Planck units are educated guesses for the kind of scale where you need to worry about effects beyond our current best physical models. This does not translate to "there is no concept of time/length/whatever smaller than the Planck one".
 
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  • #30
Ibix said:
There is no Planck (or any other) size limit in relativity. My understanding is that the various Planck units are educated guesses for the kind of scale where you need to worry about effects beyond our current best physical models. This does not translate to "there is no concept of time/length/whatever smaller than the Planck one".

Do current particle colliders use enough energy to make the relative size and lifetime of particles smaller than the Planck length & time? If not what are the smallest and shortest scales, that current particle colliders bring particles relative length and lifetime to be?
 
  • #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?
 
  • #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.
 
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  • #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.
 
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  • #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.
 
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<h2>1. What is the Planck length?</h2><p>The Planck length is a unit of measurement used in physics that represents the smallest possible length in the universe. It is approximately 1.6 x 10^-35 meters.</p><h2>2. What is the significance of the Planck length?</h2><p>The Planck length is significant because it is believed to be the scale at which the effects of quantum gravity become important. It is also the smallest length that can be measured with any degree of accuracy.</p><h2>3. What is the Planck time?</h2><p>The Planck time is a unit of measurement used in physics that represents the smallest possible unit of time in the universe. It is approximately 5.4 x 10^-44 seconds.</p><h2>4. How are the Planck length and Planck time related?</h2><p>The Planck length and Planck time are related through the Planck constant, which is a fundamental constant of nature. The Planck length is equal to the square root of the product of the Planck constant and the gravitational constant, while the Planck time is equal to the Planck length divided by the speed of light.</p><h2>5. Can the Planck length and Planck time be observed or measured?</h2><p>Currently, there is no technology or experiment that can directly observe or measure the Planck length or Planck time. However, they are important concepts in theoretical physics and are used in various equations and theories to understand the fundamental properties of the universe.</p>

1. What is the Planck length?

The Planck length is a unit of measurement used in physics that represents the smallest possible length in the universe. It is approximately 1.6 x 10^-35 meters.

2. What is the significance of the Planck length?

The Planck length is significant because it is believed to be the scale at which the effects of quantum gravity become important. It is also the smallest length that can be measured with any degree of accuracy.

3. What is the Planck time?

The Planck time is a unit of measurement used in physics that represents the smallest possible unit of time in the universe. It is approximately 5.4 x 10^-44 seconds.

4. How are the Planck length and Planck time related?

The Planck length and Planck time are related through the Planck constant, which is a fundamental constant of nature. The Planck length is equal to the square root of the product of the Planck constant and the gravitational constant, while the Planck time is equal to the Planck length divided by the speed of light.

5. Can the Planck length and Planck time be observed or measured?

Currently, there is no technology or experiment that can directly observe or measure the Planck length or Planck time. However, they are important concepts in theoretical physics and are used in various equations and theories to understand the fundamental properties of the universe.

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