# B What Is The Energy of a Point In Space?

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1. Mar 11, 2018

### abrogard

Please, moderator, just delete this question if it is too silly.

I am wondering what is happening in any one point in the SpaceTime field. That's what it is called, I think?

Because my simple understanding is that we see colours/light because of propagated electromagnetic radiation at certain frequencies.

And certain frequencies all have certain energies.

So if I see green light, say, then electromagnetic radiation of a certain energy was passing through a point in space directly before my eyes and then entered my eye. Right?

Now that point before my eye can be observed from an infinite number of places - i.e. anywhere on the surface of a sphere around that point.

And it were then the colours, i.e. the energies, perceived would be different more or less for every single observation.

So the energy you'd ascribe to that point would appear to be different for each observation post.

Could be dramatically so. From one direction - white light. From 180 degrees away it could be black.

What is going on in these points in spacetime? How are we to think of it?

2. Mar 11, 2018

### Staff: Mentor

From your question it sounds like you are interested in the energy of the electromagnetic field at a point rather than the energy of spacetime at a point. Assuming this is so, then the energy and momentum density and fluxes are described by the electromagnetic stress energy tensor.

https://en.m.wikipedia.org/wiki/Electromagnetic_stress–energy_tensor

The stress energy tensor captures the idea you mentioned about how the same field looks from different directions and at different speeds.

Last edited: Mar 11, 2018
3. Mar 11, 2018

### osilmag

The energy of a photon is E=hf where h is planck's constant and f is the frequency. So, that would be the energy of the green light you mention in your post.

4. Mar 11, 2018

What You are asking is really undefinable, a single point is really undefined in terms of energy or curvature, like asking about the volume of a 1d line, you have to add up infinite points to make up anything that can be described physicly in any way, you can however look at neigboring points at any scale to determine energy or curvature. Doing it without a framework for assigning meaning to the values is meaningless. What people mean when they talk about zero point energy is really the intrincic wobble or energy diffrances that remain when you remove all the knows «forces» from the past, aka cancalation of momentum/velocity for exsample. What remains is the energy precent when all known imputs have been cancelled out, in the case of temprature(momentum), or defining position to be constant over time you might get really a meassurment of how to enviorment fluctuates relative to what you think is a well defined possition. In the danger of sounding like langham i leave out maths here because QM is really only well defined in regimes where this flux in position(t) roughly cancel out to 0. And thus using the framework of superposition wont work of nonstatisticly sound definitive position that exsist within the plank scales. Anyway considering the actuall complexity of the vacuume if you belive in a causal structure of the uncertainy principles of qm, then you have to admit that complexity grows along with emergent structure. As an exsample imagine these kind of fluctuations on a makroscopic scale(spacial and time scales) the earth might wobble like crazy and in a matter of fractions of seconds mass distobutions would be shuffled like a snowball hitting a baloon, both waveform and masses would be distorted and complexity would rise exsponentially, this being less probable in the real world than thomas the tank engine randomly coming into exsistance to help you pass theology. Its probably safe to say that the vacuum has to have some complex form of entropy. This turned cooko quite fast, the conjecture is probably true in some sense. Points however are completly dimentionless, just abstract tools in some sence, you can use them but dont think of them as real objects. I claim no absolute or definitive knowlage of vacuum complexity but its really just an undifined way of saying what you see is causally connected in some way to the cause whether it is zero point energy or uncertainty in general.

IMO: i think the enegry absolute value of a section of space is infinite in the sense that all values that cancel completly doesnt effect anything at all our universe could ever meassure, and in a larger landscape of minima/maxima of effective vacuum energies require it to be consistant for all values and geometries of causality possible in all definable regions of space. This however doesnt really affect the mathematical structure of any 1 set of laws describing some relative reality that is aproximatly measurable. This absolute fact leads to the notion that avsolute facts arnt provable within any system, just because they contain all truth just 1 time for each absolute truth. In essense the death of philosophy in sience is real if you dont have truly ininite compatence, information and capacity to understand, that in itself is not selfconsistance, summed up we cannot ever know everything, the relation between knowlage and the physical analog is itself complexity and can never be fully defined, thos is true for math as well, tall to gödel.

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5. Mar 11, 2018

### jerromyjon

That is explained by for the most part. Relative velocity though spacetime is what changes the observed energy of waves, which is what electromagnetic radiation solely consists of.

Visibly "white" light contains many colors of the rainbow, moving towards the source would "blueshift" the light towards the ultraviolet, x-ray, gamma ray invisible range and moving away from the source would "redshift" the light into the infrared, microwave, radio wave end of the spectrum. There is no such thing as "black" light, only that which cannot be seen by our eyes.

6. Mar 11, 2018

### abrogard

Unfortunately I am so ignorant I don't know which of the two I am interested in.

Let me rephrase it:

How is it possible that there are different energies existing at the same time at one point?

Why do I think there are?

First: I think energies exist because I think an electromagnetic wave is energetic light we perceive is such a wave hence at that place in our eye where the wave excites a cell in order to initiate 'seeing' there's energy. That's in the eye. But, obviously that same packet of energy ( a photon? ) a moment ago was in a position just before the eye, outside the eye.

Second: At that position 'just outside the eye' one could imagine an observer - an eye - looking through that position from any of an infinite number of places.

Third: At each of those places they'd see something different. That signifies 'seeing', or 'absorbing' or 'interacting with' different energies.
Different even to the extent of seeing white in one direction: the full sum of light energies, and black in another: apparently zero light energy.

Fourth: Hence at that position we must conclude all these different energies exist at once. In the extreme, black and white, none and all.

I just thought I would make an attempt to clarify what I am talking about, if it makes any difference.

You have probably provided the definitive answer but unfortunately I'm unable to comprehend it. I followed the link and it is way beyond me.

Jorgenspinozasalad seems to be saying something interesting but I don't understand it, either. Unfortunately. Lots of 'unfortunately's ' here aren't there? :)

7. Mar 11, 2018

### Staff: Mentor

I agree. This is the energy of an electromagnetic field (which is well defined), not the energy of spacetime.

It doesn’t matter where you are located the energy is the same. You may not absorb it yourself if your detector is poorly positioned, but conservation of energy requires that it be there anyway. So, no, looking in different directions does not change the energy.

However, the energy will be different in different reference frames. So if you observe it from different states of motion.

At that position you would indeed conclude that all of the different energies exist at once. Not based on different directions, but based on different reference frames.

Energy is conserved, but it is not invariant.

8. Mar 11, 2018

### abrogard

This seems to me to suggest we are talking about a static detached thing which can be perceived from difference 'reference frames'.

'reference frame' just meaning 'different places' or 'different angles' to the layman, right?

But the essence of what I'm querying is that the location in question is wholly a part of a process with its own definition. i.e. a wavetrain of blue light energy. From one direction. But from another a wavetrain of red light energy. And so on.

Forget the observer. Not really what I'm asking. Just my way of trying to clarify what I'm asking.

Just consider that location. What is happening there? What IS there?

Can I impose on your patience just a little more and try one more illustration?

And a train of railroad cars - timber wagons - going through the crossing.
At any one time there's a timber wagon on the crossing.

Now the essence of this puzzle (to me) is that at any one time there's an infinite number of different trains going through that crossing.

There are flatbeds and refrigerated cars and passenger trains and every variety in between all simultaneously going through that crossing.

It is not me perceiving the fabled spaceship moving at the speed of light somewhere over there, etc, etc... with different appearances according to my reference frame.

It is not me looking at the train head on in one instance and then looking at it depart in the other.

It is not really me looking at it at all.

It is what is happening. We're told. Aren't we? Wavetrains are proceeding through that point (any point whatever, anywhere in the universe) from an infinite number of directions. Each wavetrain subject to clear definition down to measurement of energy. I think. Right?

It may be that Planck lengths and such prevent infinite division. That's fine. I don't mind. In that case talk about what's happening at the smallest length. The smallest part of that wavetrain. It gets a definite energy ascribed to it. And then we can say then, as though it occupied the whole of that area, the the energy there is that.

But then we have to consider there's an infinite number of trains passing through that place. Likewise 'Wholly' occupying that area.

What's the upshot of all that?

9. Mar 11, 2018

### Staff: Mentor

No, meaning different speeds or directions of motion. Not different places or different angles. The energy is the same under rotations or translations, but it changes under boosts.

The EM field. It is a tensor field with one given tensor value at that location.

This is incorrect. There is one train (EM field). It can be described many ways (reference frames), but there is only one train.

No, you have misunderstood somewhere

10. Mar 11, 2018

### abrogard

I have misunderstood? There are not 'wavetrains' of electromagnetic energy propagating through space?

11. Mar 11, 2018

### Staff: Mentor

At a given point in space the EM field has one definite (tensor) value. That tensor value may be due to a propagating EM wave from one or more sources located elsewhere, but there is still only one (tensor) value of the field at that point.

I missed this earlier. This does not happen. If a wave of light is blue in a given reference frame then it is blue regardless of the orientation. It is only if you boost to a different reference frame that the color may Doppler shift in the other frame.

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12. Mar 11, 2018

### abrogard

It does happen, what I'm talking about. So there's the problem between us. You're not understanding what I'm thinking of. Doubtless because my thinking is so unmathematical and so untutored it'd be unreal in your world, I guess. Causing me to ask questions that are too 'wrong' to be answered.

Let me try this:

I'm talking about what happens at a point when we shine a myriad of different coloured lights through it from a myriad of different locations all around it - a sphere.

Which is what is happening everywhere in the real world right now.

Let me ask this: does the energy of a point reflect the energy of the EM wave passing through it?

13. Mar 11, 2018

### Staff: Mentor

OK, it would have been nice if you had led with that. I thought you were talking about one emitter with detectors looking at the same light from different angles.

Not everywhere, but I get your meaning.

Yes. Again, even with your multicolor spherical emitter, there is still only one EM field value at each point. It does not matter how many sources with how many different colors converge on that point, the field still has one unique (tensor) value, as does the energy.

14. Mar 12, 2018

### abrogard

I don't have any multicolor spherical emitter. That's the nature of reality is it not? There is no point in reality that is not completely surrounded by more reality, is there? And all of reality emits radiation, right? Hence every point can be considered as at the centre of sphere being 'illuminated' by radiation.

And: back to my question.. I am asking what happens at that (ubiquitous) point?

Because you look at it from here and it appears black. No energy, let us say. You look at it from there and it appears white. Mucho energy, let us say.

What energy does it actually have?

Put it another way: How is it possible for every point to transmit radiation at all frequencies from all directions simulltaneously?

Put it another way: How can an infinite number of photons coexist at every point in the universe?

Put it another way: When a packet of energy meets an atom it causes an electron perhaps to rise to a higher energy level. According to the energy in that arriving packet. What energy arrives from these points? If white light then the energy of white light, yes, we know. If blue light then the energy from blue light, yes, we know. The point is why? That blue light was present in a point location along with much other radiation from all around and that total package - the EM field at that point? - delivers its total energy to the atom, surely, not merely the portion due to the blue light component?

The question is: What is happening in any one point... ?

15. Mar 12, 2018

### davenn

well as an example, you said you did .....

Dale has already answered that several times ... how many times need it be repeated ......

photons are not little balls/bullets shooting through space ... they don't even exist till detected by something and absorbed eg....
you eye, a radio antenna etc

As you , Dale and I sit at our computers typing all this stuff, we are "swimming" in electromagnetic radiation coming from all directions
cell phones, TV signals, AM and FM radio signals, IR Visible and UV light and radio signals from the sun and other galactic sources to name just a few.
These EM waves are passing through you all the time from all directions

If it has enough energy to do so

electromagnetic energy

you don't seem to understand or maybe you don't know/realise that light is just a part of the EM spectrum that the eye happens to be sensitive to

why what ??

forget about calling it blue/green/red or any other colour light .... colour is only assigned by our eye and brain. And what your eye/brain discriminate as say blue, could be totally different to what my eye/brain interprets the colour as, if I was, say, colour blind. What you see as blue may be red for me.
Before your eye detects a certain wavelength of EM and interprets it as a colour ... colour DOESNT EXIST
I repeat just to let it sink in for you
Before your eye detects a certain wavelength of EM and interprets it as a colour ... colour DOESNT EXIST

Honestly ... you really are not going to ask that again are you ??

Dave

16. Mar 12, 2018

### PeroK

@abrogard it's not that different from what happens with water waves, in a busy swimming pool, say. There are waves propagating in all directions, and each point on the surface of the water has a displacement equal to the sum of all the waves passing through it at that time.

Also, if you imagine a light wave travelling through space in front of you. If you are not in the path of that radiation and not detecting it in any way, doesn't mean that you can conclude that it isn't there and that region of space has no energy.

If there is another light wave crossing that path, which you do detect, then you are detecting the wave from its source. And there is no contradiction with what anyone else sees.

17. Mar 12, 2018

### abrogard

Yes: '...the sum of all the waves.. '

Are you saying that is what happens at each point in space? That is what I would expect.

In which case I'd expect an energy sum greater than that merely of the 'main' source. You can understand, I feel, if I refer to that 'main source' as a ray of coloured light for the sake of illustration (no pun intended)?

18. Mar 12, 2018

### Staff: Mentor

I have answered this several times now. It is getting frustrating repeating the answer. Once again: Regardless of how many sources are converging on a single point, the EM field at that point adds up to a single (tensor) value at that point. That single value of the field determines a single value of the energy at that point. It does not matter what direction you look at it.

Maxwells equations are linear.

Photons are bosons

Not typically, no.

And I have answered it multiple times. Please stop repeating the question and instead respond to the answer: At any one point the EM field has a single (tensor) value. That single field value corresponds to a single value for the stress energy also.

19. Mar 12, 2018

### abrogard

I post a question in good faith and I exercise politeness, restraint and refrain from any personal intimations, slights, aspersions, untoward inferences or rudenesses.

I ask no one in particular to involve themselves in interaction with me.

I repeat the question because it is not answered.

There is a single value is no answer to a question 'what happens' wherever, whenever the question. What happens when a speeding car meets a pedestrian? There is a single value. A non sequitur.

I am awaiting a response from Perok, is all.

20. Mar 12, 2018

### Staff: Mentor

And I also posted the answer in good faith. Repeatedly! Presumably your goal in asking the question was to obtain the answer, and so I provided it.

Ignoring answers and telling people to stop replying is not terribly polite. It is unfortunately inherent to the medium of communication that it is easy to become unintentionally offensive. I think that has happened to both of us here. I have become offended by your dismissal of my answer, and you have become offended by my expressed irritation. Let’s both accept the offense as unintended and concentrate on the answer.

Ok, with this response we can make progress.

So the question is about what happens to the energy at a point, the idea being that the energy perhaps has multiple values at that point depending on the direction. The energy depends on the field, and the field has a unique value at that point. Therefore the energy has a unique value also, and does not depend on the direction.

Edit: the stress energy tensor, which depends only on the field tensor, includes information not just about the energy at each point, but also about the energy flux. Detectors oriented in a particular direction would only receive energy flux in that direction. So the stress energy tensor both describes the energy at the point as well as the directional energy flux that you are confusing with the energy.

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21. Mar 12, 2018

### Khashishi

A single point is not enough to have electromagnetic waves. The physics of electromagnetic waves are described by differential equations, with both space and time derivatives. The wave behavior at a point, such as the propagation directions, doesn't just depend on the value of the field at the point, but the values in a small neighborhood around the point. You cannot simply treat space as a set of independent points.

22. Mar 12, 2018

### Khashishi

Hmm, you seem to be confusing what you see with what is actually there. You just see the light that enters your eyes. If an object is emitting more light in one direction than another, then it will look brighter from one direction than another. The object itself is losing energy equal to the total amount of light it gives out, not just the part you see.

23. Mar 12, 2018

### jerromyjon

So you think that there are infinite "degrees of freedom" around any such point you choose to specify, that have a unique point of view and can make unique observations of said point? While there are infinite values that can be observed, think about the simplistic view that every wave has a unique source and you are either looking and moving towards it or looking away and moving with it, which never happens.
In my simplified view of the situation there are only 2 relevant opposing points of view and an infinite spectrum of possibilities.

24. Mar 12, 2018

### abrogard

I surmised this might be the case. See post #8 I think it was.

No, I am not confused about that. I try to talk about a point in space. Any point in space in the centre of a sphere from which come radiations. Probably from all directions but perhaps not. Perhaps there's 'empty' areas of the universe that seem to emit no radiation. Okay. Doesn't matter to me. The point is that the point location receives radiation from a myriad of sources all around, all the time.

So what's happening at that point?

Please see post #1. I have reread it numerous times and thought how to make it clearer, simpler but finally I believe it is clear and simple enough.

If it cannot be understood in this forum then it is obviously in the wrong place. I'd be happy to move it. That'd be affected by having the moderator delete all posts and I'll raise the question elsewhere. Fine with me.

:)

25. Mar 12, 2018

### Staff: Mentor

The energy flux at that point depends on the direction, the energy does not.

Instead of a point, consider a small cubic volume with faces on the positive and negative x, y, and z directions. Energy can flow across the faces, that is energy flux. If more flows in than flows out then the energy inside increases. We can do the same with momentum. Now, take the limit as the size of the cube goes to 0 and we have the stress energy tensor at a point.

Last edited: Mar 12, 2018