# Can there be any acceleration without mass?

• B
So, we know that force equals mass times acceleration. A force is needed to cause an acceleration. I am wondering though, is mass required for accelerations to happen? Why or why not?

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Dale
Mentor
is mass required for accelerations to happen? Why or why not?
I would say yes. Anything without mass must move at c at all times. It cannot accelerate.

• fresh_42 and sophiecentaur
Anything without mass must move at c at all times. It cannot accelerate.
I don't think that this is a valid argumentation. Constant speed doesn't mean that there is no acceleration.

• Dale
sophiecentaur
Gold Member
I don't think that this is a valid argumentation. Constant speed doesn't mean that there is no acceleration.
It does. If the 'entity' only exists at velocity c then when would it be accelerating? It would emerge from whatever reaction/ interaction generated it at c. Slower than c and it would not be in existence.

It does.
Just a little hint: speed is constant for v·a=0.

sophiecentaur
Gold Member
Just a little hint: speed is constant for v·a=0.
But for 'rectilinear propagation'?
Though I must say I had ignored motion in a circle. But for 'rectilinear propagation'?
Of course linear acceleration is not possible with constant speed. However, there is Shapiro delay.

sophiecentaur
Gold Member
Of course linear acceleration is not possible with constant speed. However, there is Shapiro delay.
But the speed, measured at any point would still be c (??). Isn't that the basis of GR?

We can discuss the motion of a point under various conditions and constraints without reference to any mass at all. It makes perfect sense without reference to either force or mass.

• DrStupid and sophiecentaur
But the speed, measured at any point would still be c (??).
Yes, the locally measured speed of massless objects is always c.

sophiecentaur
Gold Member
Yes, the locally measured speed of massless objects is always c.
So where does this take the thread? Yes, the locally measured speed of massless objects is always c.
This seems like a nonsense statement. Suppose the point is at rest?

This seems like a nonsense statement. Suppose the point is at rest?
Which point are you talking about?

sophiecentaur
Gold Member
This seems like a nonsense statement. Suppose the point is at rest?
Under what circumstances could the object be at rest? What would be a 'stationary' photon be like?

Which point are you talking about?
If there is no mass, then all that exists there is a geometrical point. That is point of which I am speaking.

If there is no mass, then all that exists there is a geometrical point.
The adjective "massless" doesn't make much sense with a geometrical point. I am talking about objects that are subject to E²/c² = m²c² + p². Such objects can only be at rest with m>0 and they always move with c (locally measured) with m=0.

The adjective "massless" doesn't make much sense with a geometrical point.
The adjective "massless" applied to a geometrical point makes perfect sense. What mass do you think Euclid ascribed to a point? No, the thing that is a stretch is the idea of a mass point. The latter is a useful fiction, but it really does not make rigorous sense.

The adjective "massless" applied to a geometrical point makes perfect sense.
No, it doesn't because geometrical points never have mass. In theory you can have a point size object with mass located at a geometrical point but not a geometrical point with mass. Therefore "massless geometrical point" is a tautology.

• fresh_42
Therefore "massless geometrical point" is a tautology.
By all means, have it your way. This thread seems pretty pointless anyway.

sophiecentaur
Gold Member
The adjective "massless" doesn't make much sense with a geometrical point.
Also, a photon is not a point particle. It has no defined extent so it is pretty meaningless to assume you could use a stopwatch and push the button when it goes past. Using a very mechanical model is just not appropriate.

rcgldr
Homework Helper
What about something without a direct connection to mass, such as a shadow sweeping / accelerating across an observer's view?

sophiecentaur
Gold Member
What about something without a direct connection to mass, such as a shadow sweeping / accelerating across an observer's view?
No speed limit there! You are talking Virtual. You can let your eye travel at many times c if you scan from one galaxy to the next on a dark night.

What mass do you think Euclid ascribed to a point?
Euclid was a mathematician. His discussions dealt solely with imaginary objects.

• sophiecentaur
David, in what way do you think that points, lines, planes, etc. are imaginary objects? As I see it, they are very much real, just non-physical.

Let's try to advance in stages.

1. Material mass ##m_o## is not necessary to observe acceleration. Example. In a region of space ##\varepsilon## and ##\mu## vary from one point to another, so that there is a path where the speed of light varies. In kinematic terms you can express the acceleration of light when it crosses the region. It's acceleration without ##m_o##.

2. Light does not have ##m_o##, we know that. But do it have another type of mass? In case of having it, in the previous example there is acceleration and mass.

3. If you are interested in the fundamentals of physics and not in practical situations, in Newtonian physics and in Einstein's postulates validity is given to the conclusion obtained by Galileo, that is, in a vacuum the gravitational acceleration is independent of mass. So, an infinitesimal mass experiences the same acceleration as the finite masses. An infinitesimal mass is the limit of a mass that tends to zero. If that may correspond to your idea of "without mass", then Newton and Einstein, from the foundations of physics, are answering affirmatively to your question. The acceleration without mass is conceivable and is consistent with both theories, Newtonian and Einsteinian.

4. Is it also consistent with quantum theory? Maybe someone in the specialty can help us understand a little.