# Traveling at c-(1 planck length/planck time), then accelerate. What happens?

1. Jan 8, 2010

### Meatbot

Amateur so go easy on me.

Let's say you're traveling so close to c that you are only 1 planck length/planck time slower. Seems like you have to increase speed in increments of planck lengths/planck times (correct me if I'm wrong). Presumably to go any faster, you'd have to skip right to c since you can't increase speed by half a planck length/planck time. But since you can't travel at c, what happens to the energy if you accelerate? What about this situation would cause zero acceleration when applying thrust? Would all energy go to increasing mass and none to velocity?

I suspect it has something to do with how much energy it would take to go this fast in the first place. Seems like it would take almost all of the energy in the universe to the point where the lack of remaining energy becomes relevant. Would something prevent more energy being applied in this situation, maybe because there's simply none left or the amount that is left cannot be accessed for thrust?

Any thoughts?

Last edited: Jan 8, 2010
2. Jan 8, 2010

### tiny-tim

Hi Meatbot!
Sorry, you're wrong.

Speed isn't quantised.

(and planck length/planck time doesn't have to be small anyway, does it? )

3. Jan 8, 2010

### yuiop

First of all you have to recognise that not all Planck units are minimum possible quantities. For example the Planck mass is equivalent to millions of atoms so it is neither a minimum or a maximum. Treating the Planck length as a minimum presents difficulties such as the one you describe as well as presenting difficulties for circular or spherical objects because Pi is not a rational number. If space is divided into a grid of Planck lengths then movement in the diagonal direction would cause a problem because the square root of 2 is not rational. This does not mean that Planck units should be ignored. Photons do seem to come in quantas of energy and this can be explained in terms of the quantum of time or the Planck time interval. The frequency of a photon is an integer inverse multiple of the Planck time unit. Once you have the Planck time unit as an indivisible minimum interval, the fact that photon wavelengths are an integer multiple of the Planck length is a consequence of the Planck time interval being indivisable and the constant value of c and not a consequence of the Planck length being inherently indivisable. Now consider the motion of a particle moving at one quarter the speed of light. If light travels one Planck length in one Planck time interval, our particle will have to remain stationary for 4 Planck time intervals before jumping forward one Planck length each time it moves. If we reject the notion of the Planck length being a minimum, then our particle can travel one quarter Planck length in each Planck time interval. Using this concept, a particle can travel any fraction of a Planck length in one Planck time interval. This is in line with the very core concept at the heart of geometry and maths of the infinite divisiblity of a line. This allows an infinite range of velocities between plus and minus c and this would make "traveling so close to c that you are only 1 planck length/planck time slower" still infinitely slower than actually travelling at c. You asked for "any thoughts" and those are my thoughts on the how the kind of conflict you describe can be resolved, but maybe someone here can give you a formal answer, because I am not aware of one.

4. Jan 8, 2010

### sylas

Planck length divided by Planck time is, by definition, the speed of light!

The thread title is really saying "Start at rest, then accelerate".

Note also that if you are not accelerating, then you are indeed at rest in your own frame of reference.

5. Jan 9, 2010

### Staff: Mentor

As sylas said:
$$\frac{L_P}{T_P} = \frac{\sqrt{\frac{\hbar G}{c^3}}}{\sqrt{\frac{\hbar G}{c^5}}} = c$$
So c-c = 0

Since speeds can obviously increase in increments of less than c this must be wrong.

6. Jan 11, 2010

### Meatbot

Ok...my mistake. I meant c-[the slowest speed increment possible] which I guess is 1 planck length/life of universe. I am asking if there is a speed at which you can no longer increase speed. Is the maximum speed actually less than c by 1 planck length/life of universe.

Last edited: Jan 11, 2010
7. Jan 11, 2010

### Staff: Mentor

Consider the inertial reference frame where you are momentarily at rest right now (MCIF). There is some valid inertial reference frame which is moving at that speed wrt your MCIF. In that reference frame you are momentarily moving at that speed. What happens when you start walking? From the MCIF you gain a little momentum and a little speed, from the boosted frame you gain the same amount of momentum but almost no speed.

8. Jan 11, 2010

### Matterwave

There is no such thing as "slowest speed increment possible", as far as I know. You can go .999 (with as many 9s as you like) times the speed of light, as long as you increase the energy. Space and time are not, as far as we know, quantized (although, there may be some theories which include quantized space/time).

9. Jan 11, 2011

### ijs777

I don't know about space not being Quantised, it could be! But the best way to look at this is inertia, and what that is. When we try to accelerate something, we need to put energy into it - why? - because a photon released from that object would be released closer than the one before - an observer that you were speeding towards would see the light blue shifted, ie the frequency has gone up.

As an object tries to move from sub-light speed to light speed, it would release a new photon directly on top of the last one, ie a zero wavelength - in other words, the frequency of the light would be infinte. As far as I am aware, this equates to energy, so the object is trying to release light at an infinte frequency to an observer, thus you would need to supply it with infinite energy to make that happen, and because of E=MC2, the object would then possess infinite mass.

So my answer, which might be complete bollocks, is that each time you accelerate, the energy gets eaten up by the increase in the frequency of photons released - you have an increasing inertia which builds to infinity.

As for "you can't have half a planck length/time" well it seems that you can - its just that you can't measure it. The Planck unit is simply the degree of resolution that can be achieved. Thats where Heisenburg and his uncertainty comes into play - we have no idea whats happening in that realm. Inside the Planck time, (if the Planck time is an event) we can only say that an event is "in progress". 50% of Planck time has no measurable effect on the universe, so as an isolated "quantum" event, it hasn't "happened" but if we look at the state of play after light has travelled 10 planck lengths, our guy has gone 5 lengths. We just have no idea where he is half the time!

Last edited: Jan 11, 2011
10. Jan 11, 2011

### darkhorror

Speed is relative so you have to ask with respect to what. You will only have that speed in a certain frame of reference. In others you may be moving faster or slower. In your own frame of reference your velocity is 0.