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# A maximum rate of acceleration

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(posted in this subforum as I couldn't see where else it might fit)

I have searched around  on the net and see that this is a question that has been asked often  before and  the answer is invariably that ;

"no,there is no theoretical limit to the rate of acceleration that can be achieved." (not real quotes)

If we take a unit mass (is there such a thing? If not can we set mass at a   randomly chosen constant ?) can we say that this mass is then  subject to  a maximum rate of acceleration?

Since I imagine that mass may be a term that applies to a system rather than any one particular object then I guess I am asking  whether a given system with a given mass contains within it a maximum rate of acceleration.

Could I also ask (possibly for the second time ) if there is a theoretical mass of the whole universe? (does this mass tend to zero in a "heat death" scenario?  )

Edited by geordief
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I can't see why there should be a maximum acceleration. You can either increase the force or reduce the mass. There are, of course, practical limits!

1 hour ago, geordief said:

Could I also ask (possibly for the second time ) if there is a theoretical mass of the whole universe?

As we don't even know if it is finite, then no. There are some estimates of the lower bound of the mass of the universe but it could be infinite.

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14 minutes ago, Strange said:

I can't see why there should be a maximum acceleration. You can either increase the force or reduce the mass. There are, of course, practical limits!

As we don't even know if it is finite, then no. There are some estimates of the lower bound of the mass of the universe but it could be infinite.

But for  a given mass the available force (sourced  from within  the system) would be finite  and a function perhaps of the mass of the system. So would there be a limit then?

Can the Universe be bounded but infinite? (is there such a thing as a dynamic boundary that might apply? )

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39 minutes ago, geordief said:

But for  a given mass the available force (sourced  from within  the system) would be finite  and a function perhaps of the mass of the system. So would there be a limit then?

That would be the practical limit: using the energy of the entire universe to accelerate one neutrino, for example!

40 minutes ago, geordief said:

Can the Universe be bounded but infinite? (is there such a thing as a dynamic boundary that might apply? )

I don't think so. Infinite means that however far you go, you can always go further. So I can't see how it could be bounded. But there are all sorts of interesting paradoxes related to infinities, so maybe ... https://en.wikipedia.org/wiki/Gabriel's_Horn

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1 minute ago, Strange said:

That would be the practical limit: using the energy of the entire universe to accelerate one neutrino, for example!

I don't think so. Infinite means that however far you go, you can always go further. So I can't see how it could be bounded. But there are all sorts of interesting paradoxes related to infinities, so maybe ... https://en.wikipedia.org/wiki/Gabriel's_Horn

Yes Gabriel's Horn  does seem to show an infinite quantity enclosing a finite quantity.I think in my scenario the boundary is expanding infinitely and enclosing a finite (4D?) volume.

At T^-42 SECONDS the Universe was inflating or expanding (I  think). Was it finite or infinite then (is that a valid question?)

If it was finite then (or perhaps just  a finite times greater than earlier) how is that moment in the development of the Universe any different to say T^ +100 seconds?

Can it be expanding infinitely but finitely measurable at any "instant" (I think "instant" must be a loose term)

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18 minutes ago, geordief said:

At T^-42 SECONDS the Universe was inflating or expanding (I  think). Was it finite or infinite then (is that a valid question?)

If it is finite now, it was finite then. If it is infinite now, it was infinite then. That's all we can say.

Quote

If it was finite then (or perhaps just  a finite times greater than earlier) how is that moment in the development of the Universe any different to say T^ +100 seconds?

It was hotter and denser.

Quote

Can it be expanding infinitely but finitely measurable at any "instant" (I think "instant" must be a loose term)

Not sure what the question is. But the universe could be finite and expand forever. It would take it an infinite time to become infinite (in other words, it will never happen).

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3 hours ago, geordief said:

If we take a unit mass (is there such a thing? If not can we set mass at a   randomly chosen constant ?) can we say that this mass is then  subject to  a maximum rate of acceleration?

F=m.a   So the higher the acceleration rate, the more force you need.

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50 minutes ago, Strange said:

Not sure what the question is. But the universe could be finite and expand forever. It would take it an infinite time to become infinite (in other words, it will never happen).

Feels like you answered the question. It also feels as if  "infinity"as a word  should be  extirpated from the English  dictionary if it was practical. It seems to be an entirely  negative concept (dreamt up by some foreigner no doubt)

It seems like  shorthand for a process  rather than an actual thing in its own right.

21 minutes ago, Itoero said:

F=m.a   So the higher the acceleration rate, the more force you need.

And the force available to a finite system is also finite.....

Edited by geordief
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56 minutes ago, geordief said:

t seems like  shorthand for a process  rather than an actual thing in its own right.

Kind of. Mathematically, it can be understood by using limits. Or by using set theory. But, once you have defined infinity (as Cantor did) then that opens up a lot of interesting ways of analysing and using infinities.

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2 hours ago, geordief said:

And the force available to a finite system is also finite.....

Then the force is the limiting factor, it causes the acceleration rate.

Edited by Itoero
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26 minutes ago, Itoero said:

Then the force is the limiting factor, it causes the acceleration rate.

I was happy with the "all the universe applying force to a neutrino" as  a kind of limit. It means there is a limit of some  kind (I wonder if  the expansion/evolution of the Universe  means that the force available  to cause an acceleration in  a  part of it implies an increase in the force available or whether the greater distances involved mean that more work is  required for this hypothetical task)

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On ‎11‎-‎9‎-‎2017 at 1:48 PM, geordief said:

Could I also ask (possibly for the second time ) if there is a theoretical mass of the whole universe?

There is no theoretical mass of the whole universe because we don't know the size of the universe. People do study the mass-related properties of the observable universe.

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Is the max acceleration not relative to the space you travel in, galaxies are accelerating away from each other.

Warp drive uses a mechanism to shrink space in front of a space ship and expand it behind the ship. Warp factor 8 is 8 times the speed of light if I recall star trek correctly.

Beam me up eighth force

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15 hours ago, Handy andy said:

Is the max acceleration not relative to the space you travel in, galaxies are accelerating away from each other

The  Friedmann–Lemaître–Robertson–Walker metric shows a homogenous, isotropic expanding or contracting universe. https://arxiv.org/pdf/1203.1819.pdf This implies that all galaxies accelerate the same or differently depending on their mass,, regardless of the space they are in.

Edited by Itoero
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!

Moderator Note

Universe expansion is not what is being discussed here.

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• 2 weeks later...

The max speed of acceleration would be from Zero directly to the speed of light, nothing can travel faster than the speed of light, the energy required to do that feat for anything with mass would be infinite, lets say you had a mass of 1 kilogram as our "Test Mass", the max acceleration would be from 0 to C which is an acceleration of 299,792,458 m/s^2, the fastest you can accelerate because at the point of the speed of light your acceleration would drop to zero. This is because the Force and Energy required to accelerate yourself past the speed of light would be infinite due to Relative mass under GR, which has been proven to be correct.

Solve this equation for traveling at the speed of light, you will find that no matter your original mass your mass at the speed of light is indeed infinite or undefined, the measurements even go insane as you approach the speed of light to almost infinite numbers.

If you remember, that Force is defined as Mass * Acceleration, then to accelerate a infinite mass it would take a infinite force to accelerate it at all.  Secondly, you may say well, I can accelerate to the speed of light in as little time as I want then, well no there is limit in our universe to the smallest amount of time which is Plank Time, which is the smallest unit of time possible in the universe made from natural units. This being about 5.39106*10^-44 seconds a very short amount of time.

So, you could in theory accelerate to the speed of light in one plank time which would require a near infinite amount of Force, but in theory the max acceleration of a object is 1.03 * 10 ^ 95 m/s^2  if you were to accelerate directly from Zero to the speed of light in one plank time or 2.06*10^95 m/tp^2 if you were going the speed of light in the direction then reversed to go the speed of light in the 180 degree direction, Now you would think this is correct, but still not quite there you have failed to realize that converting to a different set of units makes this not balanced because now we are in plank units, So you have to count in Plank lengths, which Lp/tp = C which makes your max acceleration still 299,792,458 Lp/tp^2

Edited by Vmedvil
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14 minutes ago, Vmedvil said:

The max speed of acceleration would be from Zero directly to the speed of light, nothing can travel faster than the speed of light, the energy required to do that feat for anything with mass would be infinite, lets say you had a mass of 1 kilogram as our "Test Mass", the max acceleration would be from 0 to C which is an acceleration of 299,792,458 m/s^2, the fastest you can accelerate because at the point of the speed of light your acceleration would drop to zero.

There are so many things wrong with this ...

Firstly, you can't reach the speed of light!

Secondly, and more importantly, when you say that going from zero to c (*) is an acceleration of 299,792,458 m/s^2, that is only true if you achieve that speed over 1 second. What if you you reach that speed over 1/2 a second or 1/10000th of a second? The acceleration will be that much higher.

Also, you can accelerate continuously with a constant force and you will never reach the speed of light.

In your scenario you would need to apply ever increasing force to maintain the same acceleration in order to approach the speed of light.

Finally, when talking about acceleration to relativistic speeds, you need to be clear about which frame reference you are referring to. So, for example, a rocket could leave Earth and accelerate at a constant rate (say 1g) in their own frame of reference. An observer on Earth would see them approach the speed of light after about a year and the rate of acceleration steadily declining.

(*) Note: "c" not "C". The latter is carbon or degrees centigrade.

22 minutes ago, Vmedvil said:

So, you could in theory accelerate to the speed of light in one plank time which would require a near infinite amount of Force, but in theory the max acceleration of a object is

Why not half a Planck time? Or 1/1000th of a Planck time?

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10 minutes ago, Strange said:

There are so many things wrong with this ...

Firstly, you can't reach the speed of light!

Secondly, and more importantly, when you say that going from zero to c (*) is an acceleration of 299,792,458 m/s^2, that is only true if you achieve that speed over 1 second. What if you you reach that speed over 1/2 a second or 1/10000th of a second? The acceleration will be that much higher.

Also, you can accelerate continuously with a constant force and you will never reach the speed of light.

In your scenario you would need to apply ever increasing force to maintain the same acceleration in order to approach the speed of light.

Finally, when talking about acceleration to relativistic speeds, you need to be clear about which frame reference you are referring to. So, for example, a rocket could leave Earth and accelerate at a constant rate (say 1g) in their own frame of reference. An observer on Earth would see them approach the speed of light after about a year and the rate of acceleration steadily declining.

(*) Note: "c" not "C". The latter is carbon or degrees centigrade.

Why not half a Planck time? Or 1/1000th of a Planck time?

The  OP is assuming that you cannot have a time interval smaller than a Planck time:

"there is limit in our universe to the smallest amount of time which is Plank Time, which is the smallest unit of time possible in the universe made from natural units.'

That is, of course, not true.  Planck units are simply the units in which all the basic physical constants are "1".  Essentially a Planck unit of time is the time a photon would take to move the width of an electron.  There is no claim that there cannot be smaller distances, or times, or masses.

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You are right you cannot reach the speed of light but i did not want to type 9,  44 times. Plank length is the size of a unit of space the amount of space traveled moving at the speed of light in a plank time, I don't know exactly why but due to something, which I cannot for the life of me remember they are the smallest. Look into Quantum Mechanics, something to do with a photon and String, I think a plank time is the Time speed of a photon or something, which nothing can move slower than being the measurement of something moving at the speed of light's time speed being at Light's velocity.

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