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

[roineust]

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.

 

[Dale]

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.

 

[roineust]

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?

 

[Nugatory]

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.

 

[roineust]

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?

 

[roineust]

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?

 

[Dale]

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!

 

[PeroK]

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.

 

[roineust]

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?

 

[PeroK]

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?

 

[Dale]

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.

 

[roineust]

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.

 

[Dale]

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.

 

[roineust]

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.

 

[Dale]

What does this have to do with the Planck length and time. (Your last question too)

 

[Ibix]

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.

 

[roineust]

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.

 

[Vanadium 50]

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.

 

[roineust]

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?

 

[PeroK]

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.

 

[roineust]

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?

 

[PeroK]

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.

 

[Dale]

Planck size limit

There is no known size limit.

 

[Vanadium 50]

But wasn't there a whole conundrum in the past, regarding how physically real is length contraction?

Not among physicists.

 

[roineust]

Not among physicists.

https://en.wikipedia.org/wiki/Length_contraction#Reality_of_length_contraction

 

[PeroK]

https://en.wikipedia.org/wiki/Length_contraction#Reality_of_length_contraction

That's what's called a historical footnote. The "rebuttal" by A. Einstein says all that needs to be said.

 

[PeroK]

https://en.wikipedia.org/wiki/Length_contraction#Reality_of_length_contraction

Note that Einstein says: "The question as to whether length contraction really exists or not is misleading.".

That's what I was trying to tell you in post #22.

 

[Dale]

https://en.wikipedia.org/wiki/Length_contraction#Reality_of_length_contraction

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.

 

[Ibix]

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".

 

[roineust]

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?

 

[roineust]

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?

 

[Nugatory]

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.

 

[roineust]

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?

 

[Dale]

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.

 

[PeroK]

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.

 

[roineust]

Is a single occurrence of light refraction in water, considered mathematically an addition of a dimension?

 

[Nugatory]

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.

 

[PeroK]

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

 

[Thomas Sturm]

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?

 

[Ibix]

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.

 

[Thomas Sturm]

"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.