[Yahya A.Sharif (OP)]

A mass at motion moves from 0 unit to 1 unit in the number line. It must travel smaller numbers than 1 unit to reach the 1 unit. What is the smallest number it will starts with? is it 0.9 or 0.99 or 0.999? the mass must travel infinite smaller fractions to reach the 1 unit that will make it start with 0 unit and not move.

A mass at motion will change its position from one point to another point this the definition of motion , this means the two positions cannot be a point or this means it did not move and this the definition of a mass at stationary. It is not a point it is interval from a point A to a point B this interval is a length that a mass jumps.

If the mass is supposed to move from one point to a nearby point ( and it cannot move continuously) the first one is zero and the second is greater than zero then it will jump with the smallest length that is possible which is Planck length. This what calculus says the starting length must be greater than 0 and less than 1 according to length/time graph.

If Planck length is 1.6*10^-35 meters and the mass elapsed it in 1 second then the speed v is equal to 1.6*10^-35 m/s the next Planck length is 2*1.6*10^-35 m and the time interval is 2 sec ( This is constant speed) the velocity will be 1.6*10^-35 m/s which is constant. Acceleration is the rate of change in the velocity.

In case the mass jumps from point 0 to a Planck length 1.6*10^-35 in time interval equals Planck time 5.4*10-44 s then its speed must equal the speed of light 1.6*10^-35/5.4*10^-44=2.9*10^8 m/s which is the greatest speed is possible in the universe this make Planck time and length are the smallest values in the universe because the smallest time that the mass jumps from 0 to Planck length can not be smaller than  Planck time or the speed will exceed the speed of light.

A moving mass jumps with constant length which is  Planck length 1.6*10^-35 m, but time changes it is greater than or equal to Planck time so any time interval must not be less than Planck time and the length is constant which is Planck length this prove Planck time and length .

If some mass is going to start motion in the smallest time that is possible then it cannot be infinite because the mass will not start at all I must give it some time to start with which is Planck time and in other speeds less than the speed of light it will jump with Planck length from time t1 to time t2 in time interval greater than Planck time.

[Kryptid]

In my limited understanding, the Planck time and Planck length aren't necessarily the smallest possible values for time and space respectively. I think those values just represent a limit on how finely we can theoretically measure time and space. Any length or time below that scale can't be distinguished from zero. Someone do correct me if I'm wrong about that.

[Bored chemist]

The Planck mass 2.17645×10−8 Kg is really quite big.
It's 22 µg
A red blood cell weighs bout a million times less, and it has a well defined, shape + structure etc.

[Colin2B]

In my limited understanding, the Planck time and Planck length aren't necessarily the smallest possible values for time and space respectively. I think those values just represent a limit on how finely we can theoretically measure time and space. Any length or time below that scale can't be distinguished from zero. Someone do correct me if I'm wrong about that.

That’s correct, unless you are writing in a popsci mag or new theories!

[evan_au]

We really don't know if time and space are quantized or not.
- All non-quantized theories of gravity blow up near black holes; maybe a quantised theory of gravity would not? (Just like non-quantized models of the atom blew up in an "ultraviolet catastrophe"; Bohr's quantised version did not).
https://en.wikipedia.org/wiki/Bohr_model
- Some people are searching for evidence that we live in a simulated universe. Quantized space and time would be an indication to them that we live in a simulated universe of limited resolution (in both space and time).
https://en.wikipedia.org/wiki/Simulation_hypothesis

Apart from these extreme cases, both space and time seem pretty continuous on macroscopic scales.

[Kartazion]

Everything leads to believe or to confuse the infinitesimal interval vs the planck scale.

- Some people are searching for evidence that we live in a simulated universe.

Yes I agree with this idea only because theory and observation and through experience of double slits indicate so.
https://www.thenakedscientists.com/forum/index.php?topic=84146

[Yahya A.Sharif (OP)]

Thanks for your replies.
A jump for any mass at motion must be constant since it cannot exceed this value it should move from zero to a smallest amount and cannot move less than this value because it is actually  the smallest value. If something jumps this specific constant length then it must be the smallest length that is possible because it actually jumped and did not cover any smaller distance.

Even if Planck length and time are just theoretical, however the smallest length and the smallest time must exist. The jump is constant and the smallest length is possible as above. In such case we will also have a smallest time interval. Let say the smallest length is 3*10^8 meters if so the mass speed must not exceed the speed of light then a time less than 1 second does not exists.The time 1 second and a distance of 3*10^8 results in a speed of 3*10^8 m/s or the speed of light. Less than 1 second time will result in some speed greater than the speed of light.

For example 1/2 second is (3*10^8)/0.5=2*3*10^8 m/s which is greater than the speed of light. So the theory of a smallest time and distance exists.

If a mass jumps then the mass travels the smallest distance that is possible . A smallest length leads to the existence of a smallest time interval because the speed of the mass cannot exceed the speed of light. This means the theory of Max Planck is true even if the values of the smallest length and the smallest time do not have evidence.
Space-time is points of this smallest time and length.

[alancalverd]

Planck length is a number, not a limit.

Planck length has no significant meaning, physically......................... It is just a length which light travels in one unit of Planck Time.

[Yahya A.Sharif (OP)]

Planck length is a number, not a limit.

Planck length has no significant meaning, physically......................... It is just a length which light travels in one unit of Planck Time.

What happens to a moving photon starts from zero distance before Planck time? 

 If no time elapses before Planck time then time can be treated as zero value, no event happens, if time is zero then distance is also zero s=c*0=0 . In the case the length is zero before Planck time and time suddenly jumped from 0 to Planck time then the distance  will jump to some length which is Planck length   , v=s/t , s=v*t , s=c*t , "t" is Planck time which is constant, "c" is the speed of light which is also constant then "s" is also constant which is Planck length,

What happens for a moving photon after Planck time ?

Let's say Planck time is 1 second, if you measure after this 1 second  for a moving photon you will consider time as zero seconds at this jump point and you will need to start from zero and measure Planck time again. If Planck time is 1 second you cannot say the photon elapses 1.5 seconds because if you start measuring at 1 second you start measuring from zero, time cannot elapse 0.5 seconds because the smallest time elapse is Planck time 1 second. A photon elapses 1 second and at this point it starts again from zero t=0  and elapse another one second you start measuring from this 2 seconds "t=0" to measure 3 seconds, 4 units,5 units,....This exactly shows that a photon moves at discrete motion " units".

[Kartazion]

What happens for a moving photon after Planck time ?

I would have thought of putting the ends of the scale end to end (point to point) to give them the length you want.

[Kartazion]

Let's say Planck time is "t" = 1 second, if you measure after this 1 second  for a moving photon you will consider time as zero seconds at this point and you will need to start from zero and measure Planck time again. If Planck time is 1 second you cannot say the photon elapses 1.5 seconds because if you start measuring at 1 second you start measuring from zero, time cannot elapse 0.5 seconds because the smallest time elapse is Planck time 1 second. A photon elapses 1 second and at this point it starts again from zero t=0  and elapse another one second you start measuring from this 2 seconds "t=0" to measure 3 seconds, 4 units,5 units,....This exactly shows that a photon moves at discrete motion " units" and length is limited to some minimum value.

But it is very interesting to make an oscillator out of it. That is to say that when you have completed the full length, then it is back to the start in the opposite direction.

In the following graph the Planck length is between A and B:



By this principle and with a particle you to make for example quantum superposition states.

[1] https://www.nature.com/articles/s41598-022-17667-1
[2] https://www.researchgate.net/publication/281808665_Quantum_superposition_entanglement_and_state_teleportation_of_a_microorganism_on_an_electromechanical_oscillator

[evan_au]

the smallest length and the smallest time must exist

This is not a new argument. Several ancient Greek philosophers (the best-known being Zeno) produced arguments prior to 400BC, for or against continuous motion.
https://en.wikipedia.org/wiki/Zeno%27s_paradoxes

[Yahya A.Sharif (OP)]

the smallest length and the smallest time must exist

This is not a new argument. Several ancient Greek philosophers (the best-known being Zeno) produced arguments prior to 400BC, for or against continuous motion.
https://en.wikipedia.org/wiki/Zeno%27s_paradoxes

It does not matter who invented it. My theory of discrete motion solves these unsolved arguments. This theory of discrete motion is proven for a photon in reply #8. Also this theory does not just solve these paradoxes but it is supported by Planck time and Planck length reply #8 https://www.forbes.com/sites/startswithabang/2019/06/26/what-is-the-smallest-possible-distance-in-the-universe/?sh=33632ef648a1

[Georginajackson]

Planck length is a number, not a limit.

Planck length has no significant meaning, physically......................... It is just a length which light travels in one unit of Planck Time.

Thanks, that's why I wasn't getting anything, how obvious!

[Yahya A.Sharif (OP)]

Planck length is a number, not a limit.

Planck length has no significant meaning, physically......................... It is just a length which light travels in one unit of Planck Time.

Thanks, that's why I wasn't getting anything, how obvious!

https://www.forbes.com/sites/startswithabang/2019/06/26/what-is-the-smallest-possible-distance-in-the-universe/?sh=601cdaa748a1

[Kryptid]

If something is moving at half the speed of light, then it will move half a Planck length in one Planck time.

[Yahya A.Sharif (OP)]

If something is moving at half the speed of light, then it will move half a Planck length in one Planck time.

It does not need to move in Planck time It can  travel Planck length in 2*Planck time seconds, Planck time is just the smallest time that is possible. The jump will be  the constant discrete unit which is Planck length in 2*Planck time seconds.
 Did you read the article above? This article shows the smallest length that is possible which is Planck length.

[Kryptid]

It does not need to move in Planck time

So if something is moving at half the speed of light, how far will it have moved after the passage of 1 Planck time?

Planck time is just the smallest time that is possible.

We don't know that.

The jump will be  the constant discrete unit which is Planck length

We don't know that.

Did you read the article above? This article shows the smallest length that is possible which is Planck length.

That seems to be exactly the kind of "popsci" article that Colin2B was referring to. Anyway, that article admits that smaller scales could exist:

It may yet be the case that a quantum theory of gravity will reveal properties of our Universe beyond these limits...

[Yahya A.Sharif (OP)]

So if something is moving at half the speed of light, how far will it have moved after the passage of 1 Planck time?

What length a mass can travel before Planck time? It will not move because time did not elapse before Planck time. Planck time is the smallest  time that a mass can elapse reply #8. The same idea what distance the mass can travel before Planck length? It is zero because a mass cannot travel distances less than Planck length. Planck length is the smallest length that a mass can travel.
If a mass moves at half the speed of light it will not move to travel  distances less than Planck length it will wait 2*Planck time seconds to move the smallest length that is possible which is Planck length.

Planck time is just the smallest time that is possible.

We don't know that.

So why do you make arguments based on Planck time above?

Did you read the article above? This article shows the smallest length that is possible which is Planck length.

That seems to be exactly the kind of "popsci" article that Colin2B was referring to.

So what is your reference about Planck time and Planck length?

Anyway, that article admits that smaller scales could exist:

It may yet be the case that a quantum theory of gravity will reveal properties of our Universe beyond these limits...

Could exist.
Quote from the article:
"If we decide to go down to below about 10-35 meters ⁠— the Planck distance scale ⁠— our conventional laws of physics only give nonsense for answers. Here's the story of why, below a certain length scale, we cannot say anything physically meaningful."

So if something is moving at half the speed of light, how far will it have moved after the passage of 1 Planck time?

Why do you accept Planck time but not Planck length?

[evan_au]

before Planck time? It will not move

That is a classical interpretation of what is essentially a quantum measurement.

You do not know where a particle is until you measure its position.
- But there is always some uncertainty in its position, as matter has some characteristics of a wave.
- And so there is a finite probability that if you measure the position of an object, you will find that its position is different, even if its macroscopic velocity is near zero
- And you may find that in some measurements, it has moved "backwards"...

https://en.wikipedia.org/wiki/Matter_wave