Maximum speed?

• B

Summary:

The maximum speed in therory
Hello!
My kid asks if this is theoretical idea is correct and I just don't know this stuff very well:
It is impossible to travel at light speed but not impossible to travel just below. So the highest theoretical speed should be:
"The distance light has traveled in one second" minus "One Planck length"

I ask: How about "The distance light has traveled in on hour" minus "One Planck length", isn't that closer to the speed of light?

He didn't like that because he think that a Planck length is the smallest thing and cannot be divided. How should we think about this?

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ZapperZ
Staff Emeritus
Or how about the distance light travelled in one year minus a planck length? Or the distance light travelled over 13.8 billion years minus a Planck length, etc ad nauseum...

What exactly is the point in all this?

Zz.

fresh_42
Mentor
The highest possible speed is the speed of light in a vacuum (c). However, this is only achievable for particles without mass. For everything that has a mass, c can theoretically be approached as close as one has energy to accelerate the mass. But that gets soon in ranges where the total energy of the universe isn't sufficient anymore. So there is a practical limit below c, depending on the mass. The difference between any actual speed and c has nothing to do with the Planck length. The value is c, regardless whether measured in km/h, mph, lightseconds/second, lighthours/hour or whatever. This difference is a difference of speeds, hence measured in the same units. If it is close to c, then it is something like 0.999999999999999991c and the difference will be 1c-0.999999999999999991c=0.000000000000000009c and thus has the same unit as c has. There is no Planck length ansywhere.

etotheipi
Gold Member
2019 Award
speed should be:
"The distance light has traveled in one second" minus "One Planck length"
Presumably also divided by one second

berkeman
I asked him again what he meant. He says that speed cannot change less than one Planck-length per second.
I think this is the question I should have asked to begin with.

fresh_42
Mentor
This doesn't make sense. Second is an arbitrary unit. Why should it have any physical relevance? If you say Planck-length per Planck-time you end up exactly with c.

Ok, I'll try this: Can something travel less than one Planck length.

PeroK
Homework Helper
Gold Member
I asked him again what he meant. He says that speed cannot change less than one Planck-length per second.
I think this is the question I should have asked to begin with.
The Planck length and Planck time are irrelevant. It's a common misconception that you have picked up that they have some significance in this respect. Time and space are not quantised like that.

russ_watters and etotheipi
PeroK
Homework Helper
Gold Member
russ_watters and etotheipi
The Planck length and Planck time are irrelevant. It's a common misconception that you have picked up that they have some significance in this respect. Time and space are not quantised like that.
I'll use this answer and tell him that Planck length may be a smallest unit, but distances aren't a fixed number of Planck units and speeds can change less than one Planck length per second.

Thanks for helping me out, you guys are great!

etotheipi and PeroK
Staff Emeritus
2019 Award
I'll use this answer and tell him that Planck length may be a smallest unit
It may. Or the smallest length could be something else. Or there may be no smallest length.

DennisN
berkeman
Mentor
Summary:: The maximum speed in therory

It is impossible to travel at light speed but not impossible to travel just below. So the highest theoretical speed should be:
It might be helpful for your child to understand the energies required to accelerate an object to near light speed. That might help to end the "how super close" type questions. Calculate the energy it takes to accelerate even a small particle close to light speed, and you start to get an appreciation for how hard it is. Even for "theoretical" questions, you cannot exceed reasonable amounts of energy input.

russ_watters
Mentor
I'll use this answer and tell him that Planck length may be a smallest unit, but distances aren't a fixed number of Planck units and speeds can change less than one Planck length per second.

Thanks for helping me out, you guys are great!
It may. Or the smallest length could be something else. Or there may be no smallest length.
Well, it's even worse: due to time dilation and length contraction the chosen units/intervals won't necessarily be consistent with each other for different observers, or the same observer at different points in a trip.