# Maximum Acceleration

I was just wondering, is there a maximum possible acceleration? If the maximum possible speed is the speed of light, what is the smallest possible distance a particle can be accelerated through to the speed of light? Is it the Compton wavelenght? When I tried googling it I didn't find a specific answer.

Note by Manasa Kaniselvan
5 years, 4 months ago

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http://physics.stackexchange.com/questions/3334/is-there-a-maximum-possible-acceleration

- 5 years, 4 months ago

From the reply given in the link, does this mean there is an infinite acceleration but that time is discrete so that the smallest possible interval of time only allows 0 to the speed of light? I haven't yet studied the math of quantum mechanics, only the general principles...

- 5 years, 4 months ago

Actually, modern physics still uses continuous models of time (although some suggest discrete time -- Google "chronon")... anyways, the consensus there is that the "maximum" understood acceleration would be one Planck length per Planck time squared (to put in perspective, light travels 1 Planck length per Planck time), though this is dealing with extremes that we still don't understand yet.

- 5 years, 4 months ago

Well, I do not think we have any such limit given we find a source that can provide an arbitrarily large force on the particle to be accelerated.

- 5 years, 4 months ago

I haven't chimed in yet cause I wanted to see if/how people came up with an answer. If you neglect gravity then there is no maximum acceleration. If you include gravity there is. The answers in the stack exchange post referenced below are correct but not as illuminating as one might hope. I'll put it as a challenge to all of you...can you come up with a 'brilliant' argument that relies on Newtonian gravity, the fact that nothing can go faster than c, and the Heisenberg uncertainty principle? All three are needed for a maximum acceleration argument. As a starting point, imagine you are on a rocket ship in space at rest. What do you need to do to make yourself accelerate?

Staff - 5 years, 4 months ago

"There is a limit on speed, not on acceleration. Any force can not increase speed of a particle which is moving with speed of light."

- 5 years, 4 months ago

Hi, I am not a physics student but I think that there is limit to acceleration a body can have.

Let us assume that initially body was at rest so we can conclude that its initial velocity was zero.

Let us again assume that after some time it obtained maximum kinetic energy. Thus the velocity of body corresponding to maximum energy can be consider as maximum velocity, say V, of that body Thus at this point we can consider that its total energy of the body is its kinetic energy. Thus we have following equation.

$$E=1/2 m V^2…………………………………. 1$$

Here E = kinetic energy of the body = total energy of body at this instant.

m = mass of the body

and V = velocity of the body = maximum velocity of body.

$$E=m c^2……………………………….......2$$

By comparing both equation 1 and 2, We have,

$$1/2 m V^2=mc^2$$

$$V^2=2 c^2$$

$$V= √2 c$$

Thus we have the maximum velocity of the body defined as above. (I think if any body travels with this velocity then its complete mass will get changed into energy completely. Thus body will disappear as now we can see it as energy and not as mass)

Acceleration, in simple terms, is defined as the change in the velocity *of a body over an interval of *time. Thus, we have $$A=(V-0)/t$$

Replacing the V by √2 c = 4.24 (taking √2 = 1.4 and c= velocity of light= 3 ms-1 )

*We finally have *

$$A= 4.24/t$$

*Thus this can be called as the maximum possible acceleration of a body *(without converting into energy from mass completely), provided it has such mechanism which can produce such acceleration.

- 5 years, 4 months ago

it can be explained as follows: acceleration is given by: a= (v-u)/t now u and v can reach maximum up to velocity c which gives that acceleration ranges between -c to c m/s^2 . after putting value of c = v = u we get a=0 . after putting value of c = v and u =0 we get a= c . after putting value of c = u and v=0 we get a= -c . and we assume that t= 0 is not possible

- 5 years, 4 months ago

"There is a limit on speed, not on acceleration. Any force can not increase speed of a particle which is moving with speed of light."

- 5 years, 4 months ago

I'm a novice with Physics but please point out my wrongs :) . There is something I think about acceleration and matter. Biologically, if something accelerates extremely, it's components might fall apart: the cells might break up due to the miniature individual inertia of each cell. Technically, I think it is possible that there is no limit to acceleration, it can be so high that our eyes cannot see the object, so high that is can pass through a galaxy in microseconds, so fast that it will travel great distances without time passing by, a.k.a Teleporting :).

- 5 years, 4 months ago

However you have to consider that the maximum speed in the universe is the speed of light normally (so you can't really pass through a galaxy in that little time) and nothing can really be standing completely still relative to most things, which means that the maximum difference in velocity over a period of time is (very little speed) to speed of light. I think someone else here said time is taken as continuous so infinite acceleration is possible, but David M mentioned below that it's finite...

- 5 years, 4 months ago

Thank you very much for your correction. I also remembered that all EM radiations travel through space at the same speed, 2.9 * 10^8 m/s. Although I still do not think there is a limit to acceleration in my imagination but presently I think there is, as you said ma'am, the speed of light through the universe :)

- 5 years, 4 months ago

the speed of light is constant in any frame of reference, but velocity may not be. even a change in direction results in change in velocity for example reflection of light... is my idea correct?

- 5 years, 4 months ago

I believe it is :) and here comes Manasa's question, could there be a maximum possible acceleration ?

- 5 years, 4 months ago

i think there is and it is infinite, consider an example where light is passed into a room full of infinite number of reflectors or even the case of light passing into a diamond , there is a change in it's velocity from the observer's frame. but i think the acceleration would be negligible. can anyone please say if it is correct or not?

- 5 years, 4 months ago

- 5 years, 4 months ago

Mathematically it is possible in relation with Power=ForceVelocity (for Speed of light it's equal to c) Acceleration=(Power/cm) That will be The maximum acceleration i can think of,not considering the relativistic mass.

- 5 years, 4 months ago

should particle accelerate if it has mass zero...

- 5 years, 4 months ago

Sir, actually there is no massless particle but for the convienence we consider it as 0

- 5 years, 4 months ago

Isn't light considered massless?

- 5 years, 4 months ago

http://www.astronomyforum.net/blogs/astroval/67-there-maximum-possible-acceleration.html

- 5 years, 4 months ago

you Just compare old mechanics with modern physics till now classical physics cant solve this problem ( speed of light ) even quantum mechanics

- 5 years, 4 months ago

the acceleration depends on the observer. imagine two stations where 2 observers are stationed.a particle passes them with a velocity v.it passes the first observer at time t(1) and the second at t(2). therefore the time interval is dt=t(2) - t(1) rate of change of velocity in time interval dt is given by dv. then acceleration is given by a=dv/dt.......[1] if the time interval is made close to zero the acceleration becomes infinite. I think the above explanation is correct and gives the maximum acceleration - infinite.

- 5 years, 4 months ago

But wouldn't this lead to an infinite speed? I guess this also leads to postulating a smallest possible interval of time...

- 5 years, 4 months ago

No then wat do you say about photons

- 5 years, 4 months ago

I dont think its right. $$dt$$ approaching zero doesn't mean you substitute zero in the equation $$a=\frac{dv}{dt}$$. Have u learnt limits? It gives you an idea of such things. When to apply the limits and when not to..

- 5 years, 4 months ago

are you aspiring for IITJEE?

- 5 years, 4 months ago

Yes.. I am..

- 5 years, 4 months ago

yeah i know that . then how would you explain maximum acceleration? i agree my explanation was incorrect. yes i have learnt limits..

- 5 years, 4 months ago

the basic thing is light has both properties particle and wave. that's why light and other E.M. waves travel with such high speeds. matter waves such as electron waves, alpha rays have a comparatively lower speed and mechanical waves like sound waves have the lowest speed.

- 5 years, 4 months ago

I think Acceleration of a body with Escape velocity can Have maximum acceleration

- 5 years, 4 months ago

Which escape velocity Parag? Escape velocity varies according to the object we are standing on. The heavier an object is, the higher is its escape velocity. For e.g, escape velocity on sun will be much more that on earth. And we still dont know which is the heaviest object in the universe. So i dont think that escape velocity has any part in this....

- 5 years, 4 months ago

There is a mistake that speed of light is not maximum as there are even more faster rays such as Cosmic ray with accurately 3.0543*10^8 which is larger compared to light (299,792,458 m/s)the velocity can be calculated by using planck s formula and velocity of EM radiation

- 5 years, 4 months ago

Where did you find this number for cosmic rays?

Staff - 5 years, 4 months ago

It can be calculated theoritically by using the energy of Cosmic rays

- 5 years, 4 months ago

@sukruth:

The velocity of cosmic rays can go from a small fraction of the speed of light up to about .999999999999 times the speed of light, how can you say it can go further greater that speed.

- 5 years, 4 months ago