Does Planck Time Imply an Acceleration Limit?

In summary: So all inertial reference frames would be equivalent in that respect?In summary, the speed of light is the limiting factor for how fast objects can accelerate, and the Planck time is the smallest unit of time.
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Battlemage!
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Mods, I wasn't sure whether to put this in quantum physics or relativity, but since the speed of light is the limiting factor I chose here. Move wherever you think is best.

Okay so the speed of light is the asymptote for the speed that objects can accelerate to, and the Planck time is the smallest unit of time, right?

So shouldn't this put a cap on how large an acceleration an object can have? I.e., the asymptote for acceleration would have to be the speed of light divided by the Planck time, right?

Or am I missing something crucial here?

Acceleration is basically velocity divided by time, so if there is a speed limit of c and a minimum time, then doesn't there have to be an acceleration limit too?Thanks for any responses!
 
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Battlemage! said:
and the Planck time is the smallest unit of time, right?
No. Just like the Planck length is not the smallest unit of length (see our Insights article about this), the Planck time is not the smallest unit of time. (both "as far as we know", of course)
 
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Thanks for the info jtbell! Reading the Insights article right now.

EDIT- I see it's just more unit choices. While useful, not necessarily fundamental to the universe (although some of those ratios seem really important).

Anyway, this pretty much answered the question for me:

"
The simplest reason that Planck-pixels don’t make up the universe is special relativity and the idea that all inertial reference frames are equally valid. If there is a rest frame in which the matrix of these Planck-pixels is isotropic, in other frames they would be length contracted in one direction, and moving diagonally with respect to his matrix might impart angle-dependence on how you experience the universe. If an electromagnetic wave with the wavelength of one Planck length were propagating through space, its wavelength could be made even smaller by transforming to a reference frame in which the wavelength is even smaller, so the idea of rest-frame equivalence and a minimal length are inconsistent with one-another.

Reference https://www.physicsforums.com/insights/hand-wavy-discussion-planck-length/"

Obviously the same thing applies to time dilation and the Planck time, I would imagine.
 
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FAQ: Does Planck Time Imply an Acceleration Limit?

What is Planck Time?

Planck Time is the smallest unit of time that can be measured, corresponding to approximately 5.39 x 10^-44 seconds. It is defined as the time it takes for light to travel a distance of one Planck length in a vacuum.

Does Planck Time imply an acceleration limit?

Yes, according to the theory of relativity, Planck Time does imply an acceleration limit. This is because anything that moves faster than the speed of light would require an infinite amount of energy, which is not possible. Therefore, the speed of light serves as a universal speed limit and Planck Time is the smallest unit of time that can be used to measure this limit.

How does Planck Time relate to the concept of a "quantum of time"?

Planck Time is often referred to as the "quantum of time" because it is the smallest possible unit of time that can be measured. Just as Planck Time is the smallest unit of time, Planck Length is the smallest unit of length and Planck Mass is the smallest unit of mass. These three fundamental units are thought to be the building blocks of the universe and are used in theories such as quantum mechanics and general relativity.

Is there any evidence to support the existence of an acceleration limit at Planck Time?

Currently, there is no direct evidence to support the existence of an acceleration limit at Planck Time. However, many theories, such as string theory and loop quantum gravity, use Planck Time as a fundamental unit and suggest that there is indeed a limit to how fast objects can accelerate.

How does the concept of an acceleration limit at Planck Time impact our understanding of the universe?

The idea of an acceleration limit at Planck Time has significant implications for our understanding of the universe. It suggests that there are fundamental limits to the laws of physics and that our current understanding may not be complete. It also raises questions about the nature of time and the possibility of time travel, as well as the behavior of matter and energy at extremely small scales.

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