[jeffreyH (OP)]

Is it possible to build a device to apply constant acceleration to particles which could just be left to run for a period of time? I don't know if what I am asking is just nonsense.

[Bored chemist]

For how long, and how constant?
My spin dryer subjects clothes to an acceleration that's nearly constant in magnitude, but variable in direction for minutes at a time.
A charged particle between two charged plates will experience a fairly nearly constant acceleration until it hits one of the plates.

[jeffreyH (OP)]

I am thinking about over an extended period of time. Months maybe.

[Bored chemist]

The Earth is accelerating to the sun and has been for a lot of months.

[evan_au]

The ideal interplanetary (or, indeed, sub-light interstellar) spaceship would set off at a constant 1g (9.8m/s²) and continue at that acceleration for the entire journey, with a flipover maneuver at the midpoint.

It's a very comfortable acceleration for Earth-born astronauts, no problems with weak bones in transit, and a much shorter trip time than the traditional Hohman transfer orbit. After a year accelerating at this rate, you reach relativistic velocities, and start to benefit from time dilation.

The disadvantage is that it requires an enormous amount of energy, and an enormous amount of reaction mass. It almost demands hydrogen fusion or antimatter as a fuel (both of which are beyond our current technology).
Plus, if you run into a speck of dust at relativistic speeds, it puts a very big hole in your plans.

[jeffreyH (OP)]

The ideal interplanetary (or, indeed, sub-light interstellar) spaceship would set off at a constant 1g (9.8m/s²) and continue at that acceleration for the entire journey, with a flipover maneuver at the midpoint.

It's a very comfortable acceleration for Earth-born astronauts, no problems with weak bones in transit, and a much shorter trip time than the traditional Hohman transfer orbit. After a year accelerating at this rate, you reach relativistic velocities, and start to benefit from time dilation.

The disadvantage is that it requires an enormous amount of energy, and an enormous amount of reaction mass. It almost demands hydrogen fusion or antimatter as a fuel (both of which are beyond our current technology).
Plus, if you run into a speck of dust at relativistic speeds, it puts a very big hole in your plans.

While that is more in the ballpark of what I meant it misses the point. I am thinking earth based experiment.

[Bored chemist]

Well, if this is correct
https://www.calculatorsoup.com/calculators/physics/displacement_v_a_t.php
and  you want a month of acceleration in a country size laboratory you are limited to about a ten millionth of a g of acceleration.

What are you seeking to achieve?

[syhprum]

You don't even have to run into specks of dust CMBR photons begin to look like gamma rays!

[jeffreyH (OP)]

Well, if this is correct
https://www.calculatorsoup.com/calculators/physics/displacement_v_a_t.php
and  you want a month of acceleration in a country size laboratory you are limited to about a ten millionth of a g of acceleration.

What are you seeking to achieve?

I am not trying to achieve anything just asking a question. Your answer is exactly the sort of thing I was looking for. The calculator will be useful.

[jeffreyH (OP)]

https://physics.stackexchange.com/questions/130323/a-clock-in-freefall

This is a very interesting thread about time dilation. The answer by John Rennie is of particular interest since it indicates that the passage of time must stop at the event horizon since proper time = coordinate time = 0 at that point.

[Rubiksplanet]

So I'm thinking you want to keep accelerating a particle forever to try and get the highest possible speed. Ie can you keep increasing the speed of a particle forever?

You later stipulated that the accelerator be Earthbound.

There are two choices: a linear or a circular accelerator.

A linear accelerator (like the old cathode ray TV tubes or an electron microscope) simply accelerate the particle until it shoots out the end. It's difficult to say how big the largest earthbound linear accelerator could be. At some point the Earth curves away and the accelerator would point up into space. If only one part of your accelerator had to be tangential to Earth then you could accelerate linearly for the length of the universe. But then the accelerator would likely snap in at least one place due to engineering problems. (And the circular motion of Earth and sun and galaxy would have to be considered.  To make it truly linear you'd have to construct it all bendy such that it cancelled out all these circular motions.  - the bearing keeping it attached to Earth tangentially while cancelling out the galactic and stellar epicycles would be some bearing!!!)

The longest straight line you can get and be entirely within Earth is through the centre of Earth.

So that leaves circular accelerators.

For this the problem is that in a circular accelerator as the speed of the particle increases the radius of the circle increases.
(At cern they have many smaller accelerators that have increasing radii that inject the particles into the next accelerator in the chain when it's up to speed.

So the radius of your accelerator and the maximum speed you can reach are connected.

Obviously the largest circular accelerator would be the size of a great circle on Earth around the equator. (Earth is not perfectly spherical and you would need a perfect circle for this application) and that would limit your maximum speed.

But obviously, as mentioned elsewhere changing the velocity in a circle is constant acceleration. But the speed of your particle doesn't go up which is no fun at all! So ya boo to the pedants!

This leads me to another question, as the mass equivalence of a particle goes up under the Lorentz boost does this lead to a stronger gravitational field?

If we could accelerate a particle enough could we make an artificial gravity field? If this were true (and I suspect it isn't) then I would expect such an accelerator would be larger than the spaceship!

Unless!!! We can define "bendy" accelerators that were made of alternating infinitesimal sections of linear and circular accelerators at different places to create a "fractal" accelerator which had infinite length within a finite area of Earth! No matter how far you zoom in you get alternating patterns of linear and circular accelerators.

Hmmm.   Working artificial gravity? An approach to quantum gravity?

Does the sun have a fractal magnetic field?  That could be the key to nuclear fusion. Keeping particles moving around infinitely long magnetic field lines trapped inside a finite volume of space.

Lol. Should have been a theoretical physicist not a biophysicist.

No such thing as a dumb question!

Get to it team!

[Janus]

Is it possible to build a device to apply constant acceleration to particles which could just be left to run for a period of time? I don't know if what I am asking is just nonsense.

Constant as measured by the particle, or constant measured in the frame you are accelerating it relative to?

If you mean constant in the frame you are accelerating relative to, then the answer is no. For example, you can not accelerate a particle at a constant 9.8 m/sec/sec relative to you for 355 days, because that would give it a velocity relative to you of greater than c.   As you accelerate the particle, the amount of energy you need to expend to keep it accelerating at that rate relative to you goes up asymptotically as time goes along.  As you get closer to c, the energy needed approaches infinity.

If you mean as measured by the particle ( as in it measures its speed relative to the speed it had 1 sec ago as increasing at a steady rate). then yes you could accelerate it forever.  However for you, the acceleration would be continually decreasing, and even the particle could not measure its velocity as ever exceeding c relative to the frame it started in. (this is becuase of the way that velocities add.  Let's say the particle measures it velocity as being 0.99c relative to its starting point. It now accelerates to 0.01c relative to its present velocity.  Afterwards, it would measure its velocity with respect to its starting point as being (0.01+0.99)(1+.01(0.99))= ~0.990197c

Of course saying that you could continue to accelerate the particle as long as you want only means theoretically.  In practice, it is a different thing.  You are limited by your energy resources. And if you are using a circular accelerator, as the particle gains velocity it relativistic momentum increases and so does the centripetal force you will need to apply to hold it to its circular path. In the real world you won't be able to keep this up indefinitely and will need to let the particle follow its preferred straight  line trajectory.