# Length Contraction & Time Dilation Beyond Planck Scale: Correct?

• I
• Flatland
In summary, according to the speaker, if an object was traveling fast enough relative to an observer such that its length is contracted down to the Planck scale, there is no limit to the speed at which it can travel. However, there are theories that suggest that beyond the Planck scale, physical laws may no longer apply.
Flatland
If an object was traveling fast enough relative to an observer such that it's length is contracted down to the Planck scale (as with time), I would imagine that any further increase in speed would result in no more observable relativistic effects? Please correct me if I'm wrong.

No. There's no limit to speed in relativity except that it must be below c for a massive object and exactly c for a massless one. There is no problem with something being shorter than the Planck length (except that you might want to calculate the speed needed to shrink even an atom down to that size).

The Planck length is not "the shortest possible length". It's merely a "natural" unit of length composed of various fundamental constants.

But if it did contract beyond the Planck length it would be physically impossible to measure?

You want to evoke quantum gravity theories that predict no physical relevance to scales below the Planck scale?

There are the doubly special relativity theories (DSR). These are modifications of special relativity in which some particular value of energy/momentum, in addition to the speed of light, is an invariant.

However, Carlo Rovelli has argued (in the context of loop quantum gravity) that a minimal length (or area) doesn't contradict Lorentz invariance. Length and area operators are not classical quantities. They are quantum observables. If an observer measures a system as having the Plank length, it means that the system is in an eigenstate of the length operator ##L##. A boosted observer who measures the length of the same system is measuring a different observable ##L'##, which generally does not commute with ##L##. If the system is in an eigenstate of ##L##, then generally it will not be in an eigenstate of ##L'##. The eigenvalues of ##L'## will however be the same as the eigenvalues of ##L## (including the minimal value).

I have no idea how you'd directly measure the length of something even many orders of magnitude larger than that, even if it weren't moving at 0.999999999c or whatever. One could presumably build a chain of rulers moving at progressively higher speeds, each measuring the apparent length of the next, until you have one traveling at a comparable speed to your Planck-length-contracted atom that can measure it.

Relativity has no problem with things being as length contracted as you want. As far as beyond-relativity models go, you should ask in the Beyond the Standard Model forum.

Dale

## 1. What is the Planck scale and why is it important in understanding length contraction and time dilation?

The Planck scale is the smallest possible length scale in which our current laws of physics can be applied. It is important in understanding length contraction and time dilation because at this scale, the effects of these concepts become significant and cannot be ignored.

## 2. How does the concept of length contraction work at the Planck scale?

At the Planck scale, the concept of length contraction refers to the idea that the length of an object will appear to contract in the direction of motion when observed from a reference frame that is moving at speeds close to the speed of light. This is due to the effects of relativity and the distortion of space and time at this scale.

## 3. Can length contraction and time dilation occur beyond the Planck scale?

The concept of length contraction and time dilation can still occur beyond the Planck scale, but their effects become less significant and may be overshadowed by other physical phenomena at this scale, such as quantum effects.

## 4. How does time dilation play a role at the Planck scale?

At the Planck scale, time dilation refers to the idea that time will appear to slow down for an observer in a reference frame that is moving at speeds close to the speed of light. This is due to the distortion of space and time, and the fact that time is relative to the observer's reference frame.

## 5. Are there any practical implications of length contraction and time dilation beyond the Planck scale?

While the effects of length contraction and time dilation beyond the Planck scale may not be directly observable, they are important in understanding the fundamental laws of physics and can have implications in fields such as cosmology and high-energy physics. Additionally, the study of these concepts can lead to advances in technology, such as in the development of theories for quantum gravity.

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